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

• Label: 304.2.h
• Level: $304$
• Weight: $2$
• Character orbit: 304.h
• Rep. character: $\chi_{304}(303,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	46	10	36
Cusp forms	34	10	24
Eisenstein series	12	0	12

Trace form

\( 10 q - 2 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.2.h.a	$304$	$2$	304.h	76.d	$2$	$2$	$2$	$2.427$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b	$304$	$2$	304.h	76.d	$2$	$4$	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c	$304$	$2$	304.h	76.d	$2$	$4$	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(304, [\chi]) \cong \)