Space of modular forms of level 928, weight 4, and trivial character

• Label: 928.4.a
• Level: $928$
• Weight: $4$
• Character orbit: 928.a
• Rep. character: $\chi_{928}(1,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $10$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	928.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(928))\).

	Total	New	Old
Modular forms	368	84	284
Cusp forms	352	84	268
Eisenstein series	16	0	16

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

\(2\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(-\)	$-$	\(20\)
\(-\)	\(+\)	$-$	\(21\)
\(-\)	\(-\)	$+$	\(22\)
Plus space		\(+\)	\(43\)
Minus space		\(-\)	\(41\)

Trace form

\( 84 q + 716 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(928))\) 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	29
928.4.a.a	$928$	$4$	928.a	1.a	$1$	$1$	$1$	$54.754$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(-13\)	\(16\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}-13q^{5}+2^{4}q^{7}+22q^{9}-45q^{11}+\cdots\)
928.4.a.b	$928$	$4$	928.a	1.a	$1$	$1$	$1$	$54.754$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(7\)	\(-13\)	\(-16\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-13q^{5}-2^{4}q^{7}+22q^{9}+45q^{11}+\cdots\)
928.4.a.c	$928$	$4$	928.a	1.a	$1$	$8$	$8$	$54.754$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-20\)	\(0\)		$+$	$-$	$-$	$2^{10}\cdot 5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-3-\beta _{2})q^{5}+\beta _{4}q^{7}+(5+\cdots)q^{9}+\cdots\)
928.4.a.d	$928$	$4$	928.a	1.a	$1$	$9$	$9$	$54.754$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(10\)	\(-12\)		$-$	$+$	$-$	$2^{12}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
928.4.a.e	$928$	$4$	928.a	1.a	$1$	$9$	$9$	$54.754$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(10\)	\(12\)		$+$	$+$	$+$	$2^{12}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{4})q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots\)
928.4.a.f	$928$	$4$	928.a	1.a	$1$	$10$	$10$	$54.754$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$2^{14}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{6}q^{7}+(5-\beta _{5}+\cdots)q^{9}+\cdots\)
928.4.a.g	$928$	$4$	928.a	1.a	$1$	$10$	$10$	$54.754$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(40\)	\(0\)		$-$	$-$	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(4+\beta _{3})q^{5}-\beta _{8}q^{7}+(6+\beta _{2}+\cdots)q^{9}+\cdots\)
928.4.a.h	$928$	$4$	928.a	1.a	$1$	$12$	$12$	$54.754$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-14\)	\(-10\)	\(-44\)		$+$	$-$	$-$	$2^{17}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-1+\beta _{4})q^{5}+(-4+\cdots)q^{7}+\cdots\)
928.4.a.i	$928$	$4$	928.a	1.a	$1$	$12$	$12$	$54.754$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)		$+$	$+$	$+$	$2^{19}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+\beta _{7}q^{7}+(14+\cdots)q^{9}+\cdots\)
928.4.a.j	$928$	$4$	928.a	1.a	$1$	$12$	$12$	$54.754$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(14\)	\(-10\)	\(44\)		$-$	$-$	$+$	$2^{17}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-1+\beta _{4})q^{5}+(4-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(928))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(928)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 2}\)