Space of modular forms of level 1156, weight 2, and Character 1156.h

• Label: 1156.2.h
• Level: $1156$
• Weight: $2$
• Character orbit: 1156.h
• Rep. character: $\chi_{1156}(733,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $92$
• Newform subspaces: $8$
• Sturm bound: $306$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.h (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(306\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1156, [\chi])\).

	Total	New	Old
Modular forms	720	92	628
Cusp forms	504	92	412
Eisenstein series	216	0	216

Trace form

92 * q - 4 * q^5 + 4 * q^9 + 8 * q^11 + 4 * q^15 + 4 * q^19 - 8 * q^23 - 4 * q^25 + 12 * q^27 - 12 * q^29 - 24 * q^31 - 16 * q^35 - 4 * q^37 - 24 * q^39 - 4 * q^41 + 12 * q^43 + 4 * q^45 + 4 * q^49 + 28 * q^53 + 4 * q^57 + 28 * q^59 - 4 * q^61 - 4 * q^63 - 8 * q^65 + 8 * q^67 + 16 * q^69 - 16 * q^71 + 12 * q^73 - 8 * q^75 + 4 * q^77 + 8 * q^79 - 12 * q^83 + 4 * q^87 - 8 * q^91 - 28 * q^93 - 12 * q^95 - 12 * q^97 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1156, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1156.2.h.a	$1156$	$2$	1156.h	17.d	$8$	$4$	$1$	$9.231$	\(\Q(\zeta_{8})\)	None					68.2.h.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1-\zeta_{8})q^{3}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1156.2.h.b	$1156$	$2$	1156.h	17.d	$8$	$4$	$1$	$9.231$	\(\Q(\zeta_{8})\)	None					68.2.h.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-1+\zeta_{8})q^{5}+\cdots\)
1156.2.h.c	$1156$	$2$	1156.h	17.d	$8$	$4$	$1$	$9.231$	\(\Q(\zeta_{8})\)	None					68.2.h.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1+\zeta_{8})q^{3}+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1156.2.h.d	$1156$	$2$	1156.h	17.d	$8$	$8$	$2$	$9.231$	\(\Q(\zeta_{16})\)	None					68.2.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta_{3} q^{3}+2\beta_{6} q^{5}+3\beta_{7} q^{7}-\beta_{4} q^{9}+\cdots\)
1156.2.h.e	$1156$	$2$	1156.h	17.d	$8$	$16$	$4$	$9.231$	16.0.\(\cdots\).1	None					68.2.e.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	\(q-\beta _{10}q^{3}-\beta _{8}q^{5}-\beta _{15}q^{7}+(4\beta _{5}+\cdots)q^{9}+\cdots\)
1156.2.h.f	$1156$	$2$	1156.h	17.d	$8$	$16$	$4$	$9.231$	\(\Q(\zeta_{48})\)	None					68.2.a.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta_{15} q^{3}+(2\beta_{5}-\beta_{3})q^{5}-\beta_{9} q^{7}+\cdots\)
1156.2.h.g	$1156$	$2$	1156.h	17.d	$8$	$16$	$4$	$9.231$	16.0.\(\cdots\).4	None		✓			1156.2.a.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta _{6}q^{3}+(-\beta _{13}+\beta _{15})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1156.2.h.h	$1156$	$2$	1156.h	17.d	$8$	$24$	$6$	$9.231$		None		✓	✓		1156.2.a.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 2}\)