Space of modular forms of level 304, weight 2, and Character 304.be

• Label: 304.2.be
• Level: $304$
• Weight: $2$
• Character orbit: 304.be
• Rep. character: $\chi_{304}(15,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.be (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

	Total	New	Old
Modular forms	276	60	216
Cusp forms	204	60	144
Eisenstein series	72	0	72

Trace form

\( 60 q + 18 q^{9} - 12 q^{13} - 12 q^{21} + 18 q^{33} - 54 q^{41} + 30 q^{49} + 36 q^{53} + 12 q^{61} - 108 q^{65} - 96 q^{73} - 72 q^{77} - 126 q^{81} - 72 q^{85} - 36 q^{89} - 24 q^{93} - 18 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.2.be.a	$304$	$2$	304.be	76.k	$18$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			304.2.be.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b	$304$	$2$	304.be	76.k	$18$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			304.2.be.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c	$304$	$2$	304.be	76.k	$18$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			304.2.be.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d	$304$	$2$	304.be	76.k	$18$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			304.2.be.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)