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

• Label: 76.2.i
• Level: $76$
• Weight: $2$
• Character orbit: 76.i
• Rep. character: $\chi_{76}(5,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $12$
• 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.i (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
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	78	12	66
Cusp forms	42	12	30
Eisenstein series	36	0	36

Trace form

12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * 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.i.a	$76$	$2$	76.i	19.e	$9$	$12$	$2$	$0.607$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	76.2.i.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)

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

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