Space of modular forms of level 920, weight 2, and Character 920.e

• Label: 920.2.e
• Level: $920$
• Weight: $2$
• Character orbit: 920.e
• Rep. character: $\chi_{920}(369,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

	Total	New	Old
Modular forms	152	32	120
Cusp forms	136	32	104
Eisenstein series	16	0	16

Trace form

32 * q + 4 * q^5 - 28 * q^9 + 4 * q^15 + 4 * q^25 - 4 * q^29 - 8 * q^31 + 12 * q^35 + 24 * q^39 - 16 * q^45 - 48 * q^49 - 24 * q^51 - 8 * q^55 - 60 * q^59 + 40 * q^61 - 20 * q^65 + 8 * q^69 - 24 * q^71 + 48 * q^75 + 72 * q^79 + 16 * q^81 - 12 * q^85 - 24 * q^89 - 48 * q^91 + 24 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
920.2.e.a	$920$	$2$	920.e	5.b	$2$	$2$	$2$	$7.346$	\(\Q(\sqrt{-1}) \)	None		✓			920.2.e.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+(-i+2)q^{5}-3 i q^{7}+\cdots\)
920.2.e.b	$920$	$2$	920.e	5.b	$2$	$14$	$14$	$7.346$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			920.2.e.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}+\beta _{3}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
920.2.e.c	$920$	$2$	920.e	5.b	$2$	$16$	$16$	$7.346$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		920.2.e.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)