Space of modular forms of level 952, weight 2, and trivial character

• Label: 952.2.a
• Level: $952$
• Weight: $2$
• Character orbit: 952.a
• Rep. character: $\chi_{952}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(952))\).

	Total	New	Old
Modular forms	152	24	128
Cusp forms	137	24	113
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.

\(2\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(12\)	\(3\)	\(9\)		\(11\)	\(3\)	\(8\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(26\)	\(4\)	\(22\)		\(24\)	\(4\)	\(20\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(24\)	\(3\)	\(21\)		\(22\)	\(3\)	\(19\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(14\)	\(2\)	\(12\)		\(12\)	\(2\)	\(10\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(16\)	\(3\)	\(13\)		\(14\)	\(3\)	\(11\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(22\)	\(2\)	\(20\)		\(20\)	\(2\)	\(18\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(24\)	\(3\)	\(21\)		\(22\)	\(3\)	\(19\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(14\)	\(4\)	\(10\)		\(12\)	\(4\)	\(8\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(72\)	\(10\)	\(62\)		\(65\)	\(10\)	\(55\)		\(7\)	\(0\)	\(7\)
Minus space			\(-\)		\(80\)	\(14\)	\(66\)		\(72\)	\(14\)	\(58\)		\(8\)	\(0\)	\(8\)

Trace form

24 * q + 24 * q^9 + 12 * q^11 + 16 * q^15 - 16 * q^23 + 24 * q^25 + 24 * q^27 - 12 * q^29 - 8 * q^31 - 24 * q^33 - 4 * q^37 - 8 * q^39 - 8 * q^41 + 24 * q^49 + 12 * q^51 + 16 * q^53 + 8 * q^55 + 16 * q^57 - 8 * q^59 - 16 * q^61 - 8 * q^63 - 16 * q^65 + 16 * q^67 - 8 * q^69 - 24 * q^71 - 24 * q^73 - 16 * q^75 - 16 * q^79 + 16 * q^81 - 48 * q^83 - 4 * q^85 + 8 * q^87 + 16 * q^89 + 12 * q^91 - 16 * q^93 + 24 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(952))\) 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	7	17
952.2.a.a	$952$	$2$	952.a	1.a	$1$	$2$	$2$	$7.602$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	952.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
952.2.a.b	$952$	$2$	952.a	1.a	$1$	$2$	$2$	$7.602$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	952.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
952.2.a.c	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	None	✓	✓	✓	✓	952.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-2-\beta _{2})q^{5}+q^{7}+\cdots\)
952.2.a.d	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	None	✓	✓	✓	✓	952.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
952.2.a.e	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.1229.1	None	✓	✓	✓	✓	952.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
952.2.a.f	$952$	$2$	952.a	1.a	$1$	$3$	$3$	$7.602$	3.3.229.1	None	✓	✓	✓	✓	952.2.a.f	$1$	$0$	\(0\)	\(1\)	\(3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
952.2.a.g	$952$	$2$	952.a	1.a	$1$	$4$	$4$	$7.602$	4.4.5225.1	None	✓	✓	✓	✓	952.2.a.g	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}-q^{7}+\cdots\)
952.2.a.h	$952$	$2$	952.a	1.a	$1$	$4$	$4$	$7.602$	4.4.13448.1	None	✓	✓	✓	✓	952.2.a.h	$1$	$0$	\(0\)	\(3\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(1-\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(952)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)