Space of modular forms of level 76, weight 6, and trivial character

• Label: 76.6.a
• Level: $76$
• Weight: $6$
• Character orbit: 76.a
• Rep. character: $\chi_{76}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(76))\).

	Total	New	Old
Modular forms	53	7	46
Cusp forms	47	7	40
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(19\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(4\)

Trace form

\( 7 q + 2 q^{3} - 119 q^{5} + 17 q^{7} + 1067 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(76))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	19
76.6.a.a	$76$	$6$	76.a	1.a	$1$	$3$	$3$	$12.189$	3.3.272193.1	None	✓	$1$	$1$	\(0\)	\(-8\)	\(-9\)	\(-13\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b	$76$	$6$	76.a	1.a	$1$	$4$	$4$	$12.189$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(10\)	\(-110\)	\(30\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(76))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(76)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)