Space of modular forms of level 76, weight 2, and Character 76.e

• Label: 76.2.e
• Level: $76$
• Weight: $2$
• Character orbit: 76.e
• Rep. character: $\chi_{76}(45,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(76, [\chi])\).

	Total	New	Old
Modular forms	26	2	24
Cusp forms	14	2	12
Eisenstein series	12	0	12

Trace form

2 * q + q^3 + q^5 + 2 * q^9 - 8 * q^11 + q^13 - q^15 - 3 * q^17 - 8 * q^19 - 5 * q^23 + 4 * q^25 + 10 * q^27 - 7 * q^29 + 8 * q^31 - 4 * q^33 + 20 * q^37 + 2 * q^39 + 5 * q^41 + 5 * q^43 + 4 * q^45 + 7 * q^47 - 14 * q^49 + 3 * q^51 - 11 * q^53 - 4 * q^55 - q^57 - 3 * q^59 - 11 * q^61 + 2 * q^65 + 3 * q^67 - 10 * q^69 - 11 * q^71 - 15 * q^73 + 8 * q^75 + 13 * q^79 - q^81 + 3 * q^85 - 14 * q^87 - 3 * q^89 + 4 * q^93 - q^95 + 5 * q^97 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(76, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.2.e.a	$76$	$2$	76.e	19.c	$3$	$2$	$1$	$0.607$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	76.2.e.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

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