Space of modular forms of level 304, weight 1, and Character 304.e

• Label: 304.1.e
• Level: $304$
• Weight: $1$
• Character orbit: 304.e
• Rep. character: $\chi_{304}(113,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	304.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(304, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	4	1	3
Eisenstein series	6	1	5

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q - q^{5} + q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.1.e.a	$304$	$1$	304.e	19.b	$2$	$1$	$1$	$0.152$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓		✓	✓	76.1.c.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)