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

• Label: 931.2.o
• Level: $931$
• Weight: $2$
• Character orbit: 931.o
• Rep. character: $\chi_{931}(227,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
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

\( 124 q + 58 q^{4} + 9 q^{5} - 50 q^{9} + O(q^{10}) \)

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.o.a	$931$	$2$	931.o	133.o	$6$	$4$	$2$	$7.434$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-6\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
931.2.o.b	$931$	$2$	931.o	133.o	$6$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q-2\beta _{2}q^{4}-\beta _{1}q^{5}+(3-3\beta _{2})q^{9}-5\beta _{2}q^{11}+\cdots\)
931.2.o.c	$931$	$2$	931.o	133.o	$6$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+2\beta _{2})q^{4}+(1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
931.2.o.d	$931$	$2$	931.o	133.o	$6$	$4$	$2$	$7.434$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(6\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
931.2.o.e	$931$	$2$	931.o	133.o	$6$	$6$	$3$	$7.434$	6.0.6967728.1	None		$2$	$0$	\(-9\)	\(-2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
931.2.o.f	$931$	$2$	931.o	133.o	$6$	$6$	$3$	$7.434$	6.0.6967728.1	None		$2$	$0$	\(9\)	\(2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
931.2.o.g	$931$	$2$	931.o	133.o	$6$	$8$	$4$	$7.434$	8.0.592240896.1	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{4}-\beta _{6})q^{3}+(1-2\beta _{3}+\cdots)q^{4}+\cdots\)
931.2.o.h	$931$	$2$	931.o	133.o	$6$	$8$	$4$	$7.434$	8.0.592240896.1	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
931.2.o.i	$931$	$2$	931.o	133.o	$6$	$80$	$40$	$7.434$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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