Space of modular forms of level 380, weight 3, and Character 380.g

• Label: 380.3.g
• Level: $380$
• Weight: $3$
• Character orbit: 380.g
• Rep. character: $\chi_{380}(189,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(380, [\chi])\).

	Total	New	Old
Modular forms	126	20	106
Cusp forms	114	20	94
Eisenstein series	12	0	12

Trace form

\( 20 q + q^{5} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(380, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
380.3.g.a	$380$	$3$	380.g	95.d	$2$	$4$	$4$	$10.354$	\(\Q(\sqrt{-6}, \sqrt{14})\)	None		$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-5q^{5}+\beta _{2}q^{7}+5q^{9}+4q^{11}+\cdots\)
380.3.g.b	$380$	$3$	380.g	95.d	$2$	$4$	$4$	$10.354$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(9\)	\(0\)	$2^{3}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	\(q+(2-\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{7}-9q^{9}+\cdots\)
380.3.g.c	$380$	$3$	380.g	95.d	$2$	$12$	$12$	$10.354$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)