Space of modular forms of level 368, weight 2, and Character 368.c

• Label: 368.2.c
• Level: $368$
• Weight: $2$
• Character orbit: 368.c
• Rep. character: $\chi_{368}(367,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

	Total	New	Old
Modular forms	54	12	42
Cusp forms	42	12	30
Eisenstein series	12	0	12

Trace form

\( 12 q - 12 q^{9} - 12 q^{25} - 24 q^{29} + 24 q^{41} + 36 q^{49} - 24 q^{69} + 72 q^{77} - 60 q^{81} + 24 q^{85} + 24 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.2.c.a	$368$	$2$	368.c	92.b	$2$	$4$	$4$	$2.938$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		✓			368.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
368.2.c.b	$368$	$2$	368.c	92.b	$2$	$8$	$8$	$2.938$	8.0.303595776.1	None		✓	✓		368.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)