LMFDB - Space of Modular Forms of Level 8015, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	8015.a (trivial)
Character field:			$\Q$
Newforms:			$ 15 $
Sturm bound:			$1840$
Trace bound:			$3$
Distinguishing $T_p$:			$2$, $3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8015))$.

	Total	New	Old
Modular forms	924	455	469
Cusp forms	917	455	462
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.

$5$	$7$	$229$	Fricke	Dim.
$+$	$+$	$+$	$+$	$52$
$+$	$+$	$-$	$-$	$63$
$+$	$-$	$+$	$-$	$68$
$+$	$-$	$-$	$+$	$45$
$-$	$+$	$+$	$-$	$67$
$-$	$+$	$-$	$+$	$44$
$-$	$-$	$+$	$+$	$41$
$-$	$-$	$-$	$-$	$75$
Plus space			$+$	$182$
Minus space			$-$	$273$

Trace form

$ 455q + 5q^{2} + 4q^{3} + 453q^{4} - q^{5} + 20q^{6} + 3q^{7} + 33q^{8} + 471q^{9} + O(q^{10}) $

\( 455q + 5q^{2} + 4q^{3} + 453q^{4} - q^{5} + 20q^{6} + 3q^{7} + 33q^{8} + 471q^{9} - 3q^{10} + 8q^{11} + 20q^{12} - 14q^{13} + q^{14} + 453q^{16} + 14q^{17} + 25q^{18} + 12q^{19} - 7q^{20} + 20q^{22} + 32q^{23} + 12q^{24} + 455q^{25} - 2q^{26} + 64q^{27} + 21q^{28} + 22q^{29} - 4q^{30} + 16q^{31} + 81q^{32} + 72q^{33} + 26q^{34} + 7q^{35} + 481q^{36} + 2q^{37} + 4q^{38} + 68q^{39} - 15q^{40} + 38q^{41} - 12q^{42} + 12q^{43} + 20q^{44} + 3q^{45} - 32q^{46} + 8q^{47} + 4q^{48} + 455q^{49} + 5q^{50} - 4q^{51} + 14q^{52} - 30q^{53} - 16q^{54} + 4q^{55} - 3q^{56} + 24q^{57} + 22q^{58} + 28q^{59} - 12q^{60} - 30q^{61} + 16q^{62} + 7q^{63} + 509q^{64} + 14q^{65} + 24q^{66} + 28q^{67} + 114q^{68} - 8q^{69} - 3q^{70} + 16q^{71} + 149q^{72} + 38q^{73} + 46q^{74} + 4q^{75} + 76q^{76} + 20q^{77} + 72q^{78} + 12q^{79} + q^{80} + 559q^{81} + 98q^{82} - 12q^{83} - 12q^{84} - 6q^{85} + 68q^{86} - 40q^{87} + 108q^{88} - 2q^{89} - 7q^{90} - 2q^{91} + 32q^{92} + 16q^{93} + 8q^{94} - 4q^{95} + 108q^{96} + 78q^{97} + 5q^{98} - 20q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8015))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	5	7	229	$q$-expansion
8015.2.a.a	$1$	$64.000$	$\Q$	None	$-2$	$-3$	$1$	$1$	$-$	$-$	$-$	$q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots$
8015.2.a.b	$1$	$64.000$	$\Q$	None	$-1$	$-2$	$1$	$1$	$-$	$-$	$+$	$q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots$
8015.2.a.c	$1$	$64.000$	$\Q$	None	$-1$	$1$	$1$	$1$	$-$	$-$	$+$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
8015.2.a.d	$1$	$64.000$	$\Q$	None	$1$	$0$	$1$	$1$	$-$	$-$	$-$	$q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots$
8015.2.a.e	$1$	$64.000$	$\Q$	None	$1$	$2$	$-1$	$-1$	$+$	$+$	$-$	$q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots$
8015.2.a.f	$1$	$64.000$	$\Q$	None	$2$	$1$	$1$	$1$	$-$	$-$	$+$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots$
8015.2.a.g	$3$	$64.000$	3.3.148.1	None	$1$	$-1$	$-3$	$-3$	$+$	$+$	$+$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
8015.2.a.h	$38$	$64.000$		None	$-6$	$-9$	$38$	$38$	$-$	$-$	$+$
8015.2.a.i	$44$	$64.000$		None	$-2$	$0$	$44$	$-44$	$-$	$+$	$-$
8015.2.a.j	$45$	$64.000$		None	$-6$	$0$	$-45$	$45$	$+$	$-$	$-$
8015.2.a.k	$49$	$64.000$		None	$-3$	$-10$	$-49$	$-49$	$+$	$+$	$+$
8015.2.a.l	$62$	$64.000$		None	$2$	$11$	$-62$	$-62$	$+$	$+$	$-$
8015.2.a.m	$67$	$64.000$		None	$3$	$0$	$67$	$-67$	$-$	$+$	$+$
8015.2.a.n	$68$	$64.000$		None	$9$	$0$	$-68$	$68$	$+$	$-$	$+$
8015.2.a.o	$73$	$64.000$		None	$7$	$14$	$73$	$73$	$-$	$-$	$-$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8015))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(8015)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(35))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(229))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1145))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1603))$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	8015.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 15 \)
Sturm bound:			\(1840\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

\(5\)	\(7\)	\(229\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(52\)
\(+\)	\(+\)	\(-\)	\(-\)	\(63\)
\(+\)	\(-\)	\(+\)	\(-\)	\(68\)
\(+\)	\(-\)	\(-\)	\(+\)	\(45\)
\(-\)	\(+\)	\(+\)	\(-\)	\(67\)
\(-\)	\(+\)	\(-\)	\(+\)	\(44\)
\(-\)	\(-\)	\(+\)	\(+\)	\(41\)
\(-\)	\(-\)	\(-\)	\(-\)	\(75\)
Plus space			\(+\)	\(182\)
Minus space			\(-\)	\(273\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	5	7	229	$q$-expansion
8015.2.a.a	\(1\)	\(64.000\)	\(\Q\)	None	\(-2\)	\(-3\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
8015.2.a.b	\(1\)	\(64.000\)	\(\Q\)	None	\(-1\)	\(-2\)	\(1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.c	\(1\)	\(64.000\)	\(\Q\)	None	\(-1\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8015.2.a.d	\(1\)	\(64.000\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
8015.2.a.e	\(1\)	\(64.000\)	\(\Q\)	None	\(1\)	\(2\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
8015.2.a.f	\(1\)	\(64.000\)	\(\Q\)	None	\(2\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
8015.2.a.g	\(3\)	\(64.000\)	3.3.148.1	None	\(1\)	\(-1\)	\(-3\)	\(-3\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
8015.2.a.h	\(38\)	\(64.000\)		None	\(-6\)	\(-9\)	\(38\)	\(38\)	\(-\)	\(-\)	\(+\)
8015.2.a.i	\(44\)	\(64.000\)		None	\(-2\)	\(0\)	\(44\)	\(-44\)	\(-\)	\(+\)	\(-\)
8015.2.a.j	\(45\)	\(64.000\)		None	\(-6\)	\(0\)	\(-45\)	\(45\)	\(+\)	\(-\)	\(-\)
8015.2.a.k	\(49\)	\(64.000\)		None	\(-3\)	\(-10\)	\(-49\)	\(-49\)	\(+\)	\(+\)	\(+\)
8015.2.a.l	\(62\)	\(64.000\)		None	\(2\)	\(11\)	\(-62\)	\(-62\)	\(+\)	\(+\)	\(-\)
8015.2.a.m	\(67\)	\(64.000\)		None	\(3\)	\(0\)	\(67\)	\(-67\)	\(-\)	\(+\)	\(+\)
8015.2.a.n	\(68\)	\(64.000\)		None	\(9\)	\(0\)	\(-68\)	\(68\)	\(+\)	\(-\)	\(+\)
8015.2.a.o	\(73\)	\(64.000\)		None	\(7\)	\(14\)	\(73\)	\(73\)	\(-\)	\(-\)	\(-\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8015))\) 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	8015.2.a

Level	8015
Weight	2
Character orbit	a
Rep. character	\(\chi_{8015}(1,\cdot)\)
Character field	\(\Q\)
Dimension	455
Newforms	15
Sturm bound	1840
Trace bound	3