Space of modular forms of level 936, weight 2, and trivial character

• Label: 936.2.a
• Level: $936$
• Weight: $2$
• Character orbit: 936.a
• Rep. character: $\chi_{936}(1,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $12$
• Sturm bound: $336$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(336\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(936))\).

	Total	New	Old
Modular forms	184	15	169
Cusp forms	153	15	138
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(20\)	\(1\)	\(19\)		\(17\)	\(1\)	\(16\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(26\)	\(2\)	\(24\)		\(22\)	\(2\)	\(20\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)		\(23\)	\(3\)	\(20\)		\(19\)	\(3\)	\(16\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)		\(23\)	\(1\)	\(22\)		\(19\)	\(1\)	\(18\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)		\(26\)	\(1\)	\(25\)		\(22\)	\(1\)	\(21\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)		\(20\)	\(2\)	\(18\)		\(16\)	\(2\)	\(14\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)		\(23\)	\(2\)	\(21\)		\(19\)	\(2\)	\(17\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)		\(23\)	\(3\)	\(20\)		\(19\)	\(3\)	\(16\)		\(4\)	\(0\)	\(4\)
Plus space			\(+\)		\(86\)	\(6\)	\(80\)		\(71\)	\(6\)	\(65\)		\(15\)	\(0\)	\(15\)
Minus space			\(-\)		\(98\)	\(9\)	\(89\)		\(82\)	\(9\)	\(73\)		\(16\)	\(0\)	\(16\)

Trace form

15 * q - 2 * q^5 - 4 * q^7 + 4 * q^11 + q^13 + 8 * q^17 - 12 * q^23 + 19 * q^25 + 14 * q^29 - 4 * q^31 - 10 * q^35 - 14 * q^37 - 2 * q^41 + 14 * q^43 + 20 * q^47 + 33 * q^49 + 10 * q^53 + 16 * q^59 - 2 * q^61 - 4 * q^65 + 4 * q^67 + 4 * q^71 - 6 * q^73 - 24 * q^77 + 12 * q^79 + 4 * q^83 + 8 * q^85 + 22 * q^89 - 6 * q^91 + 20 * q^95 - 18 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(936))\) 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	13
936.2.a.a	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				312.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{11}-q^{13}-2q^{17}+8q^{19}+\cdots\)
936.2.a.b	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓		✓	✓	312.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{13}-2q^{17}-4q^{19}-q^{25}+\cdots\)
936.2.a.c	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓	✓	✓	✓	936.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-4q^{11}-q^{13}-2q^{19}+\cdots\)
936.2.a.d	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				312.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+2q^{11}-q^{13}+6q^{17}-4q^{19}+\cdots\)
936.2.a.e	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				312.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{11}-q^{13}-2q^{17}-4q^{23}-5q^{25}+\cdots\)
936.2.a.f	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				104.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+5q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
936.2.a.g	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓	✓	✓	✓	936.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{19}+\cdots\)
936.2.a.h	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				312.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}+q^{13}-2q^{17}+8q^{19}+\cdots\)
936.2.a.i	$936$	$2$	936.a	1.a	$1$	$1$	$1$	$7.474$	\(\Q\)	None	✓				312.2.a.d	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots\)
936.2.a.j	$936$	$2$	936.a	1.a	$1$	$2$	$2$	$7.474$	\(\Q(\sqrt{17}) \)	None	✓		✓		104.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
936.2.a.k	$936$	$2$	936.a	1.a	$1$	$2$	$2$	$7.474$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	936.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
936.2.a.l	$936$	$2$	936.a	1.a	$1$	$2$	$2$	$7.474$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	936.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+(2-\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(936)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)