Space of modular forms of level 1156, weight 4, and trivial character

• Label: 1156.4.a
• Level: $1156$
• Weight: $4$
• Character orbit: 1156.a
• Rep. character: $\chi_{1156}(1,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $12$
• Sturm bound: $612$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1156.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(612\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1156))\).

	Total	New	Old
Modular forms	486	68	418
Cusp forms	432	68	364
Eisenstein series	54	0	54

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

\(2\)	\(17\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(32\)
\(-\)	\(-\)	$+$	\(36\)
Plus space		\(+\)	\(36\)
Minus space		\(-\)	\(32\)

Trace form

\( 68 q - 2 q^{3} - 18 q^{5} + 4 q^{7} + 608 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1156))\) 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	17
1156.4.a.a	$1156$	$4$	1156.a	1.a	$1$	$1$	$1$	$68.206$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(8\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+8q^{5}+12q^{7}-23q^{9}+10q^{11}+\cdots\)
1156.4.a.b	$1156$	$4$	1156.a	1.a	$1$	$2$	$2$	$68.206$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(15\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{3}+(5+5\beta )q^{5}+(5-5\beta )q^{7}+\cdots\)
1156.4.a.c	$1156$	$4$	1156.a	1.a	$1$	$2$	$2$	$68.206$	\(\Q(\sqrt{229}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-21\)	\(-25\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-10-\beta )q^{5}+(-12+\cdots)q^{7}+\cdots\)
1156.4.a.d	$1156$	$4$	1156.a	1.a	$1$	$2$	$2$	$68.206$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4\beta q^{3}-\beta q^{5}-20\beta q^{7}+5q^{9}+2^{5}\beta q^{11}+\cdots\)
1156.4.a.e	$1156$	$4$	1156.a	1.a	$1$	$2$	$2$	$68.206$	\(\Q(\sqrt{229}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(21\)	\(25\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(10+\beta )q^{5}+(12+\beta )q^{7}+\cdots\)
1156.4.a.f	$1156$	$4$	1156.a	1.a	$1$	$2$	$2$	$68.206$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(5\)	\(-15\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(3-\beta )q^{3}+(-10+5\beta )q^{5}-5\beta q^{7}+\cdots\)
1156.4.a.g	$1156$	$4$	1156.a	1.a	$1$	$3$	$3$	$68.206$	3.3.1524.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-26\)	\(-8\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-9+\beta _{1})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1156.4.a.h	$1156$	$4$	1156.a	1.a	$1$	$4$	$4$	$68.206$	4.4.5999648.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
1156.4.a.i	$1156$	$4$	1156.a	1.a	$1$	$6$	$6$	$68.206$	6.6.889407488.2	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{2}+3\beta _{5})q^{5}+\cdots\)
1156.4.a.j	$1156$	$4$	1156.a	1.a	$1$	$12$	$12$	$68.206$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-30\)	\(18\)		$-$	$+$	$-$	$2^{6}\cdot 3\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-2-\beta _{6})q^{5}+(2+\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
1156.4.a.k	$1156$	$4$	1156.a	1.a	$1$	$12$	$12$	$68.206$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(30\)	\(-18\)		$-$	$-$	$+$	$2^{6}\cdot 3\cdot 17^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(2+\beta _{6})q^{5}+(-2-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
1156.4.a.l	$1156$	$4$	1156.a	1.a	$1$	$20$	$20$	$68.206$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{16}\cdot 17^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{13}q^{5}-\beta _{15}q^{7}+(13+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1156))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1156)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)