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

• Label: 304.2.n
• Level: $304$
• Weight: $2$
• Character orbit: 304.n
• Rep. character: $\chi_{304}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	92	20	72
Cusp forms	68	20	48
Eisenstein series	24	0	24

Trace form

\( 20 q - 16 q^{9} + O(q^{10}) \)

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.n.a	$304$	$2$	304.n	76.f	$6$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		✓			304.2.n.a	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b	$304$	$2$	304.n	76.f	$6$	$2$	$1$	$2.427$	\(\Q(\sqrt{-3}) \)	None		✓			304.2.n.a	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c	$304$	$2$	304.n	76.f	$6$	$4$	$2$	$2.427$	\(\Q(\zeta_{12})\)	None		✓			304.2.n.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d	$304$	$2$	304.n	76.f	$6$	$6$	$3$	$2.427$	6.0.31726512.1	None		✓			304.2.n.d	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e	$304$	$2$	304.n	76.f	$6$	$6$	$3$	$2.427$	6.0.31726512.1	None		✓			304.2.n.d	$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)