Space of modular forms of level 1155, weight 2, and Character 1155.q

• Label: 1155.2.q
• Level: $1155$
• Weight: $2$
• Character orbit: 1155.q
• Rep. character: $\chi_{1155}(331,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $104$
• Newform subspaces: $12$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

	Total	New	Old
Modular forms	400	104	296
Cusp forms	368	104	264
Eisenstein series	32	0	32

Trace form

\( 104 q - 4 q^{3} - 48 q^{4} - 4 q^{7} - 52 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1155.2.q.a	$1155$	$2$	1155.q	7.c	$3$	$2$	$1$	$9.223$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
1155.2.q.b	$1155$	$2$	1155.q	7.c	$3$	$2$	$1$	$9.223$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-1\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
1155.2.q.c	$1155$	$2$	1155.q	7.c	$3$	$2$	$1$	$9.223$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
1155.2.q.d	$1155$	$2$	1155.q	7.c	$3$	$2$	$1$	$9.223$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
1155.2.q.e	$1155$	$2$	1155.q	7.c	$3$	$2$	$1$	$9.223$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
1155.2.q.f	$1155$	$2$	1155.q	7.c	$3$	$4$	$2$	$9.223$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
1155.2.q.g	$1155$	$2$	1155.q	7.c	$3$	$10$	$5$	$9.223$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(5\)	\(-5\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{6}+\beta _{8})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1155.2.q.h	$1155$	$2$	1155.q	7.c	$3$	$12$	$6$	$9.223$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(6\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-\beta _{3}-\beta _{5})q^{4}+\cdots\)
1155.2.q.i	$1155$	$2$	1155.q	7.c	$3$	$14$	$7$	$9.223$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(7\)	\(-7\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(\beta _{9}+\beta _{11})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1155.2.q.j	$1155$	$2$	1155.q	7.c	$3$	$16$	$8$	$9.223$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(8\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+\beta _{3}q^{3}+(\beta _{3}-\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
1155.2.q.k	$1155$	$2$	1155.q	7.c	$3$	$18$	$9$	$9.223$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(9\)	\(9\)	\(3\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+\beta _{7})q^{3}+(-2-2\beta _{7}+\cdots)q^{4}+\cdots\)
1155.2.q.l	$1155$	$2$	1155.q	7.c	$3$	$20$	$10$	$9.223$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(-10\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{4}+\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)