Space of modular forms of level 931, weight 2, and Character 931.h

• Label: 931.2.h
• Level: $931$
• Weight: $2$
• Character orbit: 931.h
• Rep. character: $\chi_{931}(410,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $124$
• Newform subspaces: $9$
• Sturm bound: $186$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(186\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

	Total	New	Old
Modular forms	204	140	64
Cusp forms	172	124	48
Eisenstein series	32	16	16

Trace form

\( 124 q + 2 q^{2} - 3 q^{3} + 114 q^{4} + 6 q^{6} - 6 q^{8} - 53 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
931.2.h.a	$931$	$2$	931.h	133.h	$3$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
931.2.h.b	$931$	$2$	931.h	133.h	$3$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
931.2.h.c	$931$	$2$	931.h	133.h	$3$	$6$	$3$	$7.434$	6.0.309123.1	None		$2$	$0$	\(4\)	\(-1\)	\(-6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{5})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.h.d	$931$	$2$	931.h	133.h	$3$	$6$	$3$	$7.434$	6.0.309123.1	None		$2$	$0$	\(4\)	\(1\)	\(6\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.h.e	$931$	$2$	931.h	133.h	$3$	$10$	$5$	$7.434$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-3\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
931.2.h.f	$931$	$2$	931.h	133.h	$3$	$10$	$5$	$7.434$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-2\)	\(3\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(\beta _{6}+\beta _{7})q^{3}+(1+\beta _{4})q^{4}+\cdots\)
931.2.h.g	$931$	$2$	931.h	133.h	$3$	$20$	$10$	$7.434$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{8}q^{2}-\beta _{1}q^{3}+(1-\beta _{7})q^{4}+(\beta _{15}+\cdots)q^{5}+\cdots\)
931.2.h.h	$931$	$2$	931.h	133.h	$3$	$24$	$12$	$7.434$		None		$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
931.2.h.i	$931$	$2$	931.h	133.h	$3$	$40$	$20$	$7.434$		None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(931, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(931, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)