Space of modular forms of level 76, weight 3, and Character 76.c

• Label: 76.3.c
• Level: $76$
• Weight: $3$
• Character orbit: 76.c
• Rep. character: $\chi_{76}(37,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(76, [\chi])\).

	Total	New	Old
Modular forms	23	4	19
Cusp forms	17	4	13
Eisenstein series	6	0	6

Trace form

\( 4 q + q^{5} + 3 q^{7} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.3.c.a	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	\(\Q(\sqrt{-29}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b	$76$	$3$	76.c	19.b	$2$	$2$	$2$	$2.071$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(9\)	\(5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)