Space of modular forms of level 924, weight 2, and trivial character

• Label: 924.2.a
• Level: $924$
• Weight: $2$
• Character orbit: 924.a
• Rep. character: $\chi_{924}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(924))\).

	Total	New	Old
Modular forms	204	8	196
Cusp forms	181	8	173
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(4\)
Minus space				\(-\)	\(4\)

Trace form

8 * q - 8 * q^5 + 8 * q^9 - 8 * q^13 + 8 * q^19 + 8 * q^23 - 8 * q^29 - 8 * q^31 + 8 * q^35 - 8 * q^37 - 32 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 + 8 * q^49 - 8 * q^51 - 8 * q^53 + 8 * q^59 + 8 * q^65 - 24 * q^67 + 8 * q^69 - 16 * q^71 + 8 * q^73 + 16 * q^75 + 16 * q^79 + 8 * q^81 + 24 * q^85 - 8 * q^87 + 16 * q^89 - 16 * q^91 + 8 * q^93 + 24 * q^95 + 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(924))\) 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	3	7	11
924.2.a.a	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
924.2.a.b	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
924.2.a.c	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
924.2.a.d	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
924.2.a.e	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
924.2.a.f	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.f	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-7q^{13}+\cdots\)
924.2.a.g	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
924.2.a.h	$924$	$2$	924.a	1.a	$1$	$1$	$1$	$7.378$	\(\Q\)	None	✓	✓	✓	✓	924.2.a.h	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(924))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(924)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)