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

• Label: 304.2.x
• Level: $304$
• Weight: $2$
• Character orbit: 304.x
• Rep. character: $\chi_{304}(27,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $152$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 304 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	168	168	0
Cusp forms	152	152	0
Eisenstein series	16	16	0

Trace form

152 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 16 * q^7 + 24 * q^10 - 8 * q^11 - 6 * q^13 - 18 * q^14 + 2 * q^16 - 4 * q^17 - 12 * q^19 + 20 * q^20 - 24 * q^21 - 6 * q^22 - 4 * q^23 + 6 * q^24 + 44 * q^26 - 30 * q^28 - 6 * q^29 - 56 * q^30 - 36 * q^32 - 12 * q^33 + 24 * q^34 - 36 * q^35 - 2 * q^36 - 66 * q^38 - 16 * q^39 + 24 * q^40 + 6 * q^42 - 2 * q^43 + 4 * q^44 - 16 * q^45 - 6 * q^48 + 88 * q^49 - 30 * q^51 + 42 * q^52 - 6 * q^53 + 12 * q^54 - 4 * q^55 - 36 * q^58 - 6 * q^59 - 48 * q^60 - 34 * q^61 - 38 * q^62 + 52 * q^64 + 42 * q^66 - 6 * q^67 + 24 * q^68 - 120 * q^70 - 12 * q^71 + 30 * q^72 - 10 * q^74 - 66 * q^76 - 64 * q^77 + 54 * q^78 - 50 * q^80 + 40 * q^81 - 14 * q^82 - 48 * q^83 + 2 * q^85 - 6 * q^86 + 96 * q^87 - 114 * q^90 - 48 * q^91 + 2 * q^92 - 8 * q^93 + 192 * q^96 - 12 * q^97 - 18 * q^98 - 28 * q^99

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.x.a	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	None		✓			304.2.x.a	$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b	$304$	$2$	304.x	304.x	$12$	$4$	$1$	$2.427$	\(\Q(\zeta_{12})\)	None		✓			304.2.x.a	$2$	$0$	\(2\)	\(4\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c	$304$	$2$	304.x	304.x	$12$	$144$	$36$	$2.427$		None		✓	✓		304.2.x.c	$4$	$0$	\(-6\)	\(-12\)	\(2\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$