Space of modular forms of level 946, weight 2, and trivial character

• Label: 946.2.a
• Level: $946$
• Weight: $2$
• Character orbit: 946.a
• Rep. character: $\chi_{946}(1,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $11$
• Sturm bound: $264$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(264\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(946))\).

	Total	New	Old
Modular forms	136	35	101
Cusp forms	129	35	94
Eisenstein series	7	0	7

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

\(2\)	\(11\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(14\)
Minus space			\(-\)	\(21\)

Trace form

\( 35 q + q^{2} + 35 q^{4} + 2 q^{5} - 4 q^{6} - 8 q^{7} + q^{8} + 31 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(946))\) 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	11	43
946.2.a.a	$946$	$2$	946.a	1.a	$1$	$1$	$1$	$7.554$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots\)
946.2.a.b	$946$	$2$	946.a	1.a	$1$	$1$	$1$	$7.554$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
946.2.a.c	$946$	$2$	946.a	1.a	$1$	$1$	$1$	$7.554$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
946.2.a.d	$946$	$2$	946.a	1.a	$1$	$2$	$2$	$7.554$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-5\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
946.2.a.e	$946$	$2$	946.a	1.a	$1$	$2$	$2$	$7.554$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-2\)	\(1\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
946.2.a.f	$946$	$2$	946.a	1.a	$1$	$2$	$2$	$7.554$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+\beta )q^{5}+\cdots\)
946.2.a.g	$946$	$2$	946.a	1.a	$1$	$4$	$4$	$7.554$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	$1$	$1$	\(4\)	\(-4\)	\(-6\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
946.2.a.h	$946$	$2$	946.a	1.a	$1$	$4$	$4$	$7.554$	4.4.13676.1	None	✓	$1$	$0$	\(4\)	\(1\)	\(1\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots\)
946.2.a.i	$946$	$2$	946.a	1.a	$1$	$5$	$5$	$7.554$	5.5.727024.1	None	✓	$1$	$1$	\(-5\)	\(1\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots\)
946.2.a.j	$946$	$2$	946.a	1.a	$1$	$6$	$6$	$7.554$	6.6.262888000.1	None	✓	$1$	$0$	\(-6\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{5})q^{5}-\beta _{1}q^{6}+\cdots\)
946.2.a.k	$946$	$2$	946.a	1.a	$1$	$7$	$7$	$7.554$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(3\)	\(8\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(946))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(946)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 2}\)