Space of modular forms of level 312, weight 4, and Character 312.m

• Label: 312.4.m
• Level: $312$
• Weight: $4$
• Character orbit: 312.m
• Rep. character: $\chi_{312}(181,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(312, [\chi])\).

	Total	New	Old
Modular forms	172	84	88
Cusp forms	164	84	80
Eisenstein series	8	0	8

Trace form

84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(312, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
312.4.m.a	$312$	$4$	312.m	104.e	$2$	$84$	$84$	$18.409$		None		✓	✓	✓	312.4.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)