LMFDB - Space of Modular Forms of Level 6026, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	6026.a (trivial)
Character field:			$\Q$
Newforms:			$ 13 $
Sturm bound:			$1584$
Trace bound:			$5$
Distinguishing $T_p$:			$3$, $5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6026))$.

	Total	New	Old
Modular forms	796	241	555
Cusp forms	789	241	548
Eisenstein series	7	0	7

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

$2$	$23$	$131$	Fricke	Dim.
$+$	$+$	$+$	$+$	$25$
$+$	$+$	$-$	$-$	$36$
$+$	$-$	$+$	$-$	$34$
$+$	$-$	$-$	$+$	$25$
$-$	$+$	$+$	$-$	$37$
$-$	$+$	$-$	$+$	$23$
$-$	$-$	$+$	$+$	$20$
$-$	$-$	$-$	$-$	$41$
Plus space			$+$	$93$
Minus space			$-$	$148$

Trace form

$241q $ $\mathstrut +\mathstrut q^{2} $ $\mathstrut +\mathstrut 241q^{4} $ $\mathstrut -\mathstrut 2q^{5} $ $\mathstrut -\mathstrut 4q^{6} $ $\mathstrut +\mathstrut 8q^{7} $ $\mathstrut +\mathstrut q^{8} $ $\mathstrut +\mathstrut 257q^{9} $ $\mathstrut +\mathstrut 6q^{10} $ $\mathstrut +\mathstrut 4q^{11} $ $\mathstrut +\mathstrut 18q^{13} $ $\mathstrut +\mathstrut 16q^{15} $ $\mathstrut +\mathstrut 241q^{16} $ $\mathstrut +\mathstrut 18q^{17} $ $\mathstrut -\mathstrut 3q^{18} $ $\mathstrut +\mathstrut 12q^{19} $ $\mathstrut -\mathstrut 2q^{20} $ $\mathstrut +\mathstrut 32q^{21} $ $\mathstrut -\mathstrut 4q^{22} $ $\mathstrut -\mathstrut q^{23} $ $\mathstrut -\mathstrut 4q^{24} $ $\mathstrut +\mathstrut 243q^{25} $ $\mathstrut -\mathstrut 2q^{26} $ $\mathstrut +\mathstrut 8q^{28} $ $\mathstrut +\mathstrut 6q^{29} $ $\mathstrut -\mathstrut 24q^{30} $ $\mathstrut +\mathstrut 16q^{31} $ $\mathstrut +\mathstrut q^{32} $ $\mathstrut -\mathstrut 12q^{33} $ $\mathstrut +\mathstrut 2q^{34} $ $\mathstrut +\mathstrut 4q^{35} $ $\mathstrut +\mathstrut 257q^{36} $ $\mathstrut +\mathstrut 22q^{37} $ $\mathstrut -\mathstrut 12q^{38} $ $\mathstrut +\mathstrut 36q^{39} $ $\mathstrut +\mathstrut 6q^{40} $ $\mathstrut -\mathstrut 14q^{41} $ $\mathstrut +\mathstrut 4q^{43} $ $\mathstrut +\mathstrut 4q^{44} $ $\mathstrut +\mathstrut 58q^{45} $ $\mathstrut +\mathstrut 3q^{46} $ $\mathstrut +\mathstrut 249q^{49} $ $\mathstrut +\mathstrut 39q^{50} $ $\mathstrut +\mathstrut 16q^{51} $ $\mathstrut +\mathstrut 18q^{52} $ $\mathstrut +\mathstrut 18q^{53} $ $\mathstrut -\mathstrut 40q^{54} $ $\mathstrut -\mathstrut 40q^{55} $ $\mathstrut +\mathstrut 40q^{57} $ $\mathstrut +\mathstrut 2q^{58} $ $\mathstrut -\mathstrut 16q^{59} $ $\mathstrut +\mathstrut 16q^{60} $ $\mathstrut +\mathstrut 38q^{61} $ $\mathstrut +\mathstrut 8q^{62} $ $\mathstrut +\mathstrut 28q^{63} $ $\mathstrut +\mathstrut 241q^{64} $ $\mathstrut +\mathstrut 20q^{65} $ $\mathstrut +\mathstrut 16q^{66} $ $\mathstrut -\mathstrut 4q^{67} $ $\mathstrut +\mathstrut 18q^{68} $ $\mathstrut -\mathstrut 4q^{69} $ $\mathstrut -\mathstrut 48q^{70} $ $\mathstrut +\mathstrut 8q^{71} $ $\mathstrut -\mathstrut 3q^{72} $ $\mathstrut +\mathstrut 18q^{73} $ $\mathstrut -\mathstrut 2q^{74} $ $\mathstrut -\mathstrut 12q^{75} $ $\mathstrut +\mathstrut 12q^{76} $ $\mathstrut -\mathstrut 8q^{77} $ $\mathstrut +\mathstrut 8q^{78} $ $\mathstrut +\mathstrut 40q^{79} $ $\mathstrut -\mathstrut 2q^{80} $ $\mathstrut +\mathstrut 297q^{81} $ $\mathstrut +\mathstrut 2q^{82} $ $\mathstrut +\mathstrut 4q^{83} $ $\mathstrut +\mathstrut 32q^{84} $ $\mathstrut +\mathstrut 4q^{85} $ $\mathstrut -\mathstrut 12q^{86} $ $\mathstrut +\mathstrut 24q^{87} $ $\mathstrut -\mathstrut 4q^{88} $ $\mathstrut -\mathstrut 34q^{89} $ $\mathstrut -\mathstrut 2q^{90} $ $\mathstrut +\mathstrut 56q^{91} $ $\mathstrut -\mathstrut q^{92} $ $\mathstrut +\mathstrut 56q^{93} $ $\mathstrut -\mathstrut 16q^{94} $ $\mathstrut +\mathstrut 32q^{95} $ $\mathstrut -\mathstrut 4q^{96} $ $\mathstrut +\mathstrut 10q^{97} $ $\mathstrut +\mathstrut 25q^{98} $ $\mathstrut -\mathstrut 12q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6026))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	23	131	$q$-expansion
6026.2.a.a	$1$	$48.118$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+2q^{11}-2q^{13}+\cdots$
6026.2.a.b	$1$	$48.118$	$\Q$	None	$-1$	$0$	$3$	$-2$	$+$	$+$	$+$	$q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots$
6026.2.a.c	$1$	$48.118$	$\Q$	None	$1$	$-2$	$3$	$2$	$-$	$+$	$-$	$q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots$
6026.2.a.d	$1$	$48.118$	$\Q$	None	$1$	$2$	$-1$	$2$	$-$	$+$	$-$	$q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots$
6026.2.a.e	$2$	$48.118$	$\Q(\sqrt{3}) $	None	$2$	$2$	$0$	$4$	$-$	$+$	$+$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots$
6026.2.a.f	$20$	$48.118$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$20$	$-5$	$-6$	$-12$	$-$	$-$	$+$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
6026.2.a.g	$21$	$48.118$		None	$21$	$0$	$-13$	$-18$	$-$	$+$	$-$
6026.2.a.h	$24$	$48.118$		None	$-24$	$-1$	$-1$	$-7$	$+$	$+$	$+$
6026.2.a.i	$25$	$48.118$		None	$-25$	$-4$	$-3$	$-11$	$+$	$-$	$-$
6026.2.a.j	$33$	$48.118$		None	$-33$	$3$	$-4$	$11$	$+$	$-$	$+$
6026.2.a.k	$35$	$48.118$		None	$35$	$-3$	$10$	$14$	$-$	$+$	$+$
6026.2.a.l	$36$	$48.118$		None	$-36$	$4$	$1$	$13$	$+$	$+$	$-$
6026.2.a.m	$41$	$48.118$		None	$41$	$4$	$9$	$12$	$-$	$-$	$-$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6026))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(6026)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(23))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(46))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(131))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(262))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(3013))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	6026.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 13 \)
Sturm bound:			\(1584\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

\(2\)	\(23\)	\(131\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(25\)
\(+\)	\(+\)	\(-\)	\(-\)	\(36\)
\(+\)	\(-\)	\(+\)	\(-\)	\(34\)
\(+\)	\(-\)	\(-\)	\(+\)	\(25\)
\(-\)	\(+\)	\(+\)	\(-\)	\(37\)
\(-\)	\(+\)	\(-\)	\(+\)	\(23\)
\(-\)	\(-\)	\(+\)	\(+\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(41\)
Plus space			\(+\)	\(93\)
Minus space			\(-\)	\(148\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	23	131	$q$-expansion
6026.2.a.a	\(1\)	\(48.118\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
6026.2.a.b	\(1\)	\(48.118\)	\(\Q\)	None	\(-1\)	\(0\)	\(3\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
6026.2.a.c	\(1\)	\(48.118\)	\(\Q\)	None	\(1\)	\(-2\)	\(3\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
6026.2.a.d	\(1\)	\(48.118\)	\(\Q\)	None	\(1\)	\(2\)	\(-1\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
6026.2.a.e	\(2\)	\(48.118\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(2\)	\(0\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\)
6026.2.a.f	\(20\)	\(48.118\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(20\)	\(-5\)	\(-6\)	\(-12\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
6026.2.a.g	\(21\)	\(48.118\)		None	\(21\)	\(0\)	\(-13\)	\(-18\)	\(-\)	\(+\)	\(-\)
6026.2.a.h	\(24\)	\(48.118\)		None	\(-24\)	\(-1\)	\(-1\)	\(-7\)	\(+\)	\(+\)	\(+\)
6026.2.a.i	\(25\)	\(48.118\)		None	\(-25\)	\(-4\)	\(-3\)	\(-11\)	\(+\)	\(-\)	\(-\)
6026.2.a.j	\(33\)	\(48.118\)		None	\(-33\)	\(3\)	\(-4\)	\(11\)	\(+\)	\(-\)	\(+\)
6026.2.a.k	\(35\)	\(48.118\)		None	\(35\)	\(-3\)	\(10\)	\(14\)	\(-\)	\(+\)	\(+\)
6026.2.a.l	\(36\)	\(48.118\)		None	\(-36\)	\(4\)	\(1\)	\(13\)	\(+\)	\(+\)	\(-\)
6026.2.a.m	\(41\)	\(48.118\)		None	\(41\)	\(4\)	\(9\)	\(12\)	\(-\)	\(-\)	\(-\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6026))\) 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	6026.2.a

Level	6026
Weight	2
Character orbit	a
Rep. character	\(\chi_{6026}(1,\cdot)\)
Character field	\(\Q\)
Dimension	241
Newforms	13
Sturm bound	1584
Trace bound	5