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

• Label: 931.2.i
• Level: $931$
• Weight: $2$
• Character orbit: 931.i
• Rep. character: $\chi_{931}(411,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $124$
• Newform subspaces: $8$
• Sturm bound: $186$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(186\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

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 + 3 * q^3 - 110 * q^4 - 12 * q^6 - 53 * q^9 - 12 * q^10 + 3 * q^11 - 6 * q^12 + 6 * q^13 + 21 * q^15 + 86 * q^16 + 18 * q^17 + 15 * q^18 + 12 * q^22 + 15 * q^23 + 18 * q^24 - 76 * q^25 + 3 * q^26 - 18 * q^27 - 30 * q^29 - 19 * q^30 - 15 * q^31 + 6 * q^33 - 12 * q^34 + 25 * q^36 + 18 * q^37 - 6 * q^38 + 14 * q^39 + 18 * q^41 + 20 * q^43 - 12 * q^44 - 42 * q^45 + 30 * q^46 + 36 * q^47 + 45 * q^48 + 3 * q^51 - 3 * q^52 - 27 * q^55 + 51 * q^57 + 49 * q^58 - 24 * q^59 - 30 * q^60 - 18 * q^61 - 51 * q^62 - 118 * q^64 - 51 * q^65 - 39 * q^68 + 6 * q^69 + 45 * q^71 - 180 * q^72 + 87 * q^73 + 51 * q^74 + 45 * q^75 + 90 * q^76 - 99 * q^78 + 6 * q^81 - 24 * q^82 - 43 * q^85 + 60 * q^86 - 9 * q^87 + 18 * q^88 + 3 * q^89 + 69 * q^90 - 36 * q^92 + 64 * q^93 - 66 * q^94 + 9 * q^95 + 72 * q^96 - 21 * q^97 + 33 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
931.2.i.a	$931$	$2$	931.i	133.i	$6$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None					133.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-q^{4}+(2+\cdots)q^{6}+\cdots\)
931.2.i.b	$931$	$2$	931.i	133.i	$6$	$2$	$1$	$7.434$	\(\Q(\sqrt{-3}) \)	None					133.2.i.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{6}+\cdots\)
931.2.i.c	$931$	$2$	931.i	133.i	$6$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					133.2.p.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
931.2.i.d	$931$	$2$	931.i	133.i	$6$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					133.2.i.c	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
931.2.i.e	$931$	$2$	931.i	133.i	$6$	$4$	$2$	$7.434$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					133.2.p.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.i.f	$931$	$2$	931.i	133.i	$6$	$12$	$6$	$7.434$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					133.2.p.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{6}+\beta _{9})q^{2}+(-\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots\)
931.2.i.g	$931$	$2$	931.i	133.i	$6$	$16$	$8$	$7.434$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					133.2.i.d	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}-\beta _{9})q^{3}+\cdots\)
931.2.i.h	$931$	$2$	931.i	133.i	$6$	$80$	$40$	$7.434$		None		✓	✓		931.2.p.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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