LMFDB - Space of modular forms of level 6050, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6050 = 2 \cdot 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6050.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 92 $
Sturm bound:			$1980$
Trace bound:			$19$
Distinguishing $T_p$:			$3$, $7$, $13$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6050))$.

	Total	New	Old
Modular forms	1062	173	889
Cusp forms	919	173	746
Eisenstein series	143	0	143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$5$	$11$	Fricke	Dim
$+$	$+$	$+$	$+$	$18$
$+$	$+$	$-$	$-$	$24$
$+$	$-$	$+$	$-$	$23$
$+$	$-$	$-$	$+$	$22$
$-$	$+$	$+$	$-$	$24$
$-$	$+$	$-$	$+$	$16$
$-$	$-$	$+$	$+$	$19$
$-$	$-$	$-$	$-$	$27$
Plus space			$+$	$75$
Minus space			$-$	$98$

Trace form

$ 173 q - q^{2} + 2 q^{3} + 173 q^{4} - 2 q^{6} + 8 q^{7} - q^{8} + 177 q^{9} + O(q^{10}) $

$ 173 q - q^{2} + 2 q^{3} + 173 q^{4} - 2 q^{6} + 8 q^{7} - q^{8} + 177 q^{9} + 2 q^{12} + 2 q^{13} - 4 q^{14} + 173 q^{16} - 10 q^{17} - 13 q^{18} + 18 q^{19} - 4 q^{21} - 12 q^{23} - 2 q^{24} - 16 q^{27} + 8 q^{28} - 2 q^{29} + 12 q^{31} - q^{32} + 177 q^{36} + 16 q^{37} + 2 q^{38} + 24 q^{39} + 4 q^{42} + 12 q^{43} + 12 q^{46} + 2 q^{48} + 189 q^{49} - 18 q^{51} + 2 q^{52} + 12 q^{53} - 2 q^{54} - 4 q^{56} - 4 q^{58} - 38 q^{59} + 26 q^{61} + 8 q^{62} + 8 q^{63} + 173 q^{64} + 50 q^{67} - 10 q^{68} - 52 q^{69} - 36 q^{71} - 13 q^{72} - 2 q^{73} + 18 q^{74} + 18 q^{76} + 28 q^{79} + 173 q^{81} - 6 q^{82} - 12 q^{83} - 4 q^{84} - 18 q^{86} - 32 q^{87} - 52 q^{89} + 120 q^{91} - 12 q^{92} + 52 q^{93} + 16 q^{94} - 2 q^{96} + 50 q^{97} - 25 q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6050))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6050.2.a.a	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.b	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.c	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.d	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.e	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.f	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.g	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
6050.2.a.h	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
6050.2.a.i	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots$
6050.2.a.j	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{9}+q^{13}+\cdots$
6050.2.a.k	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{9}+q^{13}+\cdots$
6050.2.a.l	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
6050.2.a.m	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
6050.2.a.n	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-4q^{7}-q^{8}+\cdots$
6050.2.a.o	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.p	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.q	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.r	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.s	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+2q^{7}-q^{8}+\cdots$
6050.2.a.t	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$3$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-5q^{7}-q^{8}+\cdots$
6050.2.a.u	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.v	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.w	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.x	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.y	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.z	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.ba	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bb	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+4q^{7}+q^{8}+\cdots$
6050.2.a.bc	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bd	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6050.2.a.be	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{13}+\cdots$
6050.2.a.bf	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{13}+\cdots$
6050.2.a.bg	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
6050.2.a.bh	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
6050.2.a.bi	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
6050.2.a.bj	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bk	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bl	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-2q^{7}+q^{8}+\cdots$
6050.2.a.bm	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bn	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bo	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bp	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bq	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+5q^{7}+q^{8}+\cdots$
6050.2.a.br	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$2$	$-2$	$-3$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.bs	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-3$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.bt	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
6050.2.a.bu	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}+q^{4}+2\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
6050.2.a.bv	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}+q^{4}+2\beta q^{6}-\beta q^{7}+\cdots$
6050.2.a.bw	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
6050.2.a.bx	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+2\beta )q^{7}+\cdots$
6050.2.a.by	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(1+2\beta )q^{7}+\cdots$
6050.2.a.bz	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+3q^{7}-q^{8}+\cdots$
6050.2.a.ca	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(-1+2\beta )q^{7}+\cdots$
6050.2.a.cb	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$-2$	$1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}-q^{8}+\cdots$
6050.2.a.cc	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$2$	$0$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.cd	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$2$	$0$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.ce	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}-2\beta q^{6}-\beta q^{7}+\cdots$
6050.2.a.cf	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$2$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.cg	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$3$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.ch	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$3$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.ci	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.cj	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-3$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
6050.2.a.ck	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
6050.2.a.cl	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}+q^{4}-2\beta q^{6}+\beta q^{7}+\cdots$
6050.2.a.cm	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}+q^{4}-2\beta q^{6}+(1+\beta )q^{7}+\cdots$
6050.2.a.cn	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
6050.2.a.co	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(1-2\beta )q^{7}+\cdots$
6050.2.a.cp	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}-3q^{7}+q^{8}+\cdots$
6050.2.a.cq	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(-1-2\beta )q^{7}+\cdots$
6050.2.a.cr	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(1-2\beta )q^{7}+\cdots$
6050.2.a.cs	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.ct	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+\beta q^{7}+\cdots$
6050.2.a.cu	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.cv	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.cw	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$3$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.cx	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$3$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.cy	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.5225.1	None	✓	$1$	$0$	$-4$	$-3$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
6050.2.a.cz	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.2525.1	None	✓	$1$	$0$	$-4$	$-3$	$0$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots$
6050.2.a.da	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.28400.1	None	✓	$1$	$1$	$-4$	$-2$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
6050.2.a.db	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.35136.1	None	✓	$1$	$0$	$-4$	$-2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$
6050.2.a.dc	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$2$	$0$	$-4$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(2+\beta _{3})q^{7}+\cdots$
6050.2.a.dd	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.28400.1	None	✓	$1$	$0$	$-4$	$2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
6050.2.a.de	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.35136.1	None	✓	$1$	$1$	$-4$	$2$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots$
6050.2.a.df	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.2525.1	None	✓	$1$	$0$	$-4$	$3$	$0$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
6050.2.a.dg	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.2525.1	None	✓	$1$	$0$	$4$	$-3$	$0$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots$
6050.2.a.dh	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.5225.1	None	✓	$1$	$0$	$4$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
6050.2.a.di	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.28400.1	None	✓	$1$	$1$	$4$	$-2$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-1+\cdots)q^{7}+\cdots$
6050.2.a.dj	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.35136.1	None	✓	$1$	$1$	$4$	$-2$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
6050.2.a.dk	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$2$	$1$	$4$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-2+\cdots)q^{7}+\cdots$
6050.2.a.dl	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.28400.1	None	✓	$1$	$0$	$4$	$2$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+(-1+\cdots)q^{7}+\cdots$
6050.2.a.dm	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.35136.1	None	✓	$1$	$0$	$4$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$
6050.2.a.dn	$6050$	$2$	6050.a	1.a	$1$	$4$	$4$	$48.309$	4.4.2525.1	None	✓	$1$	$0$	$4$	$3$	$0$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6050))$ into lower level spaces

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6050 = 2 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6050.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 92 \)
Sturm bound:			\(1980\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\), \(17\), \(19\)

\(2\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(18\)
\(+\)	\(+\)	\(-\)	$-$	\(24\)
\(+\)	\(-\)	\(+\)	$-$	\(23\)
\(+\)	\(-\)	\(-\)	$+$	\(22\)
\(-\)	\(+\)	\(+\)	$-$	\(24\)
\(-\)	\(+\)	\(-\)	$+$	\(16\)
\(-\)	\(-\)	\(+\)	$+$	\(19\)
\(-\)	\(-\)	\(-\)	$-$	\(27\)
Plus space			\(+\)	\(75\)
Minus space			\(-\)	\(98\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6050))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6050))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	6050.2.a

Level	$6050$
Weight	$2$
Character orbit	6050.a
Rep. character	$\chi_{6050}(1,\cdot)$
Character field	$\Q$
Dimension	$173$
Newform subspaces	$92$
Sturm bound	$1980$
Trace bound	$19$