Space of modular forms of level 928, weight 2, and trivial character

• Label: 928.2.a
• Level: $928$
• Weight: $2$
• Character orbit: 928.a
• Rep. character: $\chi_{928}(1,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(928))\).

	Total	New	Old
Modular forms	128	28	100
Cusp forms	113	28	85
Eisenstein series	15	0	15

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(31\)	\(7\)	\(24\)		\(28\)	\(7\)	\(21\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)		\(33\)	\(8\)	\(25\)		\(29\)	\(8\)	\(21\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(33\)	\(7\)	\(26\)		\(29\)	\(7\)	\(22\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(31\)	\(6\)	\(25\)		\(27\)	\(6\)	\(21\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(62\)	\(13\)	\(49\)		\(55\)	\(13\)	\(42\)		\(7\)	\(0\)	\(7\)
Minus space		\(-\)		\(66\)	\(15\)	\(51\)		\(58\)	\(15\)	\(43\)		\(8\)	\(0\)	\(8\)

Trace form

28 * q + 36 * q^9 - 16 * q^13 + 8 * q^17 - 16 * q^21 + 28 * q^25 - 16 * q^33 - 16 * q^37 - 8 * q^41 - 48 * q^45 + 28 * q^49 - 48 * q^53 - 16 * q^61 + 48 * q^65 - 16 * q^69 + 8 * q^73 - 16 * q^77 + 60 * q^81 - 16 * q^85 + 24 * q^89 + 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(928))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	29
928.2.a.a	$928$	$2$	928.a	1.a	$1$	$1$	$1$	$7.410$	\(\Q\)	None	✓	✓			928.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+5q^{11}+q^{13}+\cdots\)
928.2.a.b	$928$	$2$	928.a	1.a	$1$	$1$	$1$	$7.410$	\(\Q\)	None	✓	✓			928.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-5q^{11}+q^{13}+\cdots\)
928.2.a.c	$928$	$2$	928.a	1.a	$1$	$2$	$2$	$7.410$	\(\Q(\sqrt{2}) \)	None	✓	✓			928.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2q^{7}-2\beta q^{9}+\cdots\)
928.2.a.d	$928$	$2$	928.a	1.a	$1$	$2$	$2$	$7.410$	\(\Q(\sqrt{5}) \)	None	✓	✓			928.2.a.d	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+3q^{5}+2q^{9}+\beta q^{11}+q^{13}+\cdots\)
928.2.a.e	$928$	$2$	928.a	1.a	$1$	$2$	$2$	$7.410$	\(\Q(\sqrt{2}) \)	None	✓	✓			928.2.a.c	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2q^{7}+2\beta q^{9}+(1+\cdots)q^{11}+\cdots\)
928.2.a.f	$928$	$2$	928.a	1.a	$1$	$4$	$4$	$7.410$	\(\Q(\zeta_{20})^+\)	None	✓	✓	✓		928.2.a.f	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
928.2.a.g	$928$	$2$	928.a	1.a	$1$	$5$	$5$	$7.410$	5.5.230224.1	None	✓	✓	✓		928.2.a.g	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
928.2.a.h	$928$	$2$	928.a	1.a	$1$	$5$	$5$	$7.410$	5.5.230224.1	None	✓	✓	✓		928.2.a.g	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(4\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{4}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
928.2.a.i	$928$	$2$	928.a	1.a	$1$	$6$	$6$	$7.410$	6.6.68772992.1	None	✓	✓	✓		928.2.a.i	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(2-\beta _{5})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(928))\) into lower level spaces

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