Space of modular forms of level 7920, weight 2, and Character 7920.f

• Label: 7920.2.f
• Level: $7920$
• Weight: $2$
• Character orbit: 7920.f
• Rep. character: $\chi_{7920}(3761,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $3456$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7920.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(3456\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7920, [\chi])\).

	Total	New	Old
Modular forms	1776	96	1680
Cusp forms	1680	96	1584
Eisenstein series	96	0	96

Trace form

\( 96 q - 96 q^{25} - 96 q^{49} + 32 q^{67} - 96 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7920, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7920.2.f.a	$7920$	$2$	7920.f	33.d	$2$	$8$	$8$	$63.242$	8.0.4328587264.1	None					990.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{5}-\beta _{7})q^{7}+(2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7920.2.f.b	$7920$	$2$	7920.f	33.d	$2$	$8$	$8$	$63.242$	8.0.4328587264.1	None					990.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-\beta _{5}-\beta _{7})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
7920.2.f.c	$7920$	$2$	7920.f	33.d	$2$	$12$	$12$	$63.242$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					3960.2.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(\beta _{1}+\beta _{9})q^{11}+\cdots\)
7920.2.f.d	$7920$	$2$	7920.f	33.d	$2$	$12$	$12$	$63.242$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					3960.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+(-\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)
7920.2.f.e	$7920$	$2$	7920.f	33.d	$2$	$12$	$12$	$63.242$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					3960.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}+(-\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)
7920.2.f.f	$7920$	$2$	7920.f	33.d	$2$	$12$	$12$	$63.242$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					3960.2.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(-\beta _{1}-\beta _{9}+\cdots)q^{11}+\cdots\)
7920.2.f.g	$7920$	$2$	7920.f	33.d	$2$	$16$	$16$	$63.242$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					495.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+(\beta _{1}+\beta _{14})q^{7}+(\beta _{4}+\beta _{5}+\cdots)q^{11}+\cdots\)
7920.2.f.h	$7920$	$2$	7920.f	33.d	$2$	$16$	$16$	$63.242$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					1980.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(-\beta _{7}-\beta _{10})q^{7}+(-\beta _{8}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1584, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3960, [\chi])\)\(^{\oplus 2}\)