Space of modular forms of level 961, weight 2, and Character 961.c

• Label: 961.2.c
• Level: $961$
• Weight: $2$
• Character orbit: 961.c
• Rep. character: $\chi_{961}(439,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $126$
• Newform subspaces: $12$
• Sturm bound: $165$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(165\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(961, [\chi])\).

	Total	New	Old
Modular forms	198	182	16
Cusp forms	134	126	8
Eisenstein series	64	56	8

Trace form

126 * q + 4 * q^2 - 2 * q^3 + 96 * q^4 + 2 * q^5 + 6 * q^6 + 2 * q^7 + 18 * q^8 - 35 * q^9 - 5 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 9 * q^14 + 4 * q^15 + 28 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 - q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 - 13 * q^25 - 6 * q^26 + 4 * q^27 + 7 * q^28 + 16 * q^29 - 12 * q^30 - 60 * q^32 - 28 * q^33 - 2 * q^34 + 8 * q^35 + 26 * q^36 + 2 * q^37 - 5 * q^38 + 20 * q^39 - 12 * q^40 - 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 4 * q^45 - 16 * q^46 - 4 * q^47 - 6 * q^48 + 17 * q^49 + 5 * q^50 - 6 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 - 16 * q^56 - 2 * q^57 - 10 * q^59 + 20 * q^60 - 60 * q^63 - 46 * q^64 - 2 * q^65 - 44 * q^66 - 8 * q^67 + 10 * q^68 + 4 * q^69 + 42 * q^70 - 22 * q^71 - 23 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 17 * q^76 + 28 * q^77 - 4 * q^78 - 22 * q^79 - 3 * q^80 + 49 * q^81 - 41 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 8 * q^87 + 18 * q^88 + 16 * q^89 - 23 * q^90 - 12 * q^91 + 16 * q^92 - 68 * q^94 + 8 * q^95 - 2 * q^96 - 24 * q^97 - 11 * q^98 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(961, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
961.2.c.a	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					31.2.c.a	$2$	$0$	\(-4\)	\(-2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
961.2.c.b	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			961.2.a.b	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}-q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots\)
961.2.c.c	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					31.2.a.a	$2$	$0$	\(2\)	\(-2\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
961.2.c.d	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					31.2.d.a	$2$	$0$	\(2\)	\(-2\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
961.2.c.e	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					31.2.a.a	$2$	$0$	\(2\)	\(2\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
961.2.c.f	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					31.2.d.a	$2$	$0$	\(2\)	\(2\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(1+\beta _{3})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
961.2.c.g	$961$	$2$	961.c	31.c	$3$	$6$	$3$	$7.674$	6.0.2101707.2	\(\Q(\sqrt{-31}) \)		✓			961.2.a.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{3}]$	\(q+\beta _{2}q^{2}+(2+\beta _{1})q^{4}+(-\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
961.2.c.h	$961$	$2$	961.c	31.c	$3$	$8$	$4$	$7.674$	8.0.207360000.1	None		✓			961.2.a.h	$4$	$0$	\(12\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\beta _{2})q^{2}-\beta _{1}q^{3}+(3-3\beta _{2})q^{4}+\cdots\)
961.2.c.i	$961$	$2$	961.c	31.c	$3$	$16$	$8$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(-3\)	\(-3\)	\(2\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{6}-\beta _{9}+\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
961.2.c.j	$961$	$2$	961.c	31.c	$3$	$16$	$8$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(3\)	\(-3\)	\(2\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(1+\beta _{6}+\beta _{9}-\beta _{10}+\beta _{11}+\cdots)q^{3}+\cdots\)
961.2.c.k	$961$	$2$	961.c	31.c	$3$	$24$	$12$	$7.674$		None		✓			961.2.a.k	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{3}]$
961.2.c.l	$961$	$2$	961.c	31.c	$3$	$32$	$16$	$7.674$		None		✓	✓		961.2.a.l	$4$	$0$	\(-16\)	\(0\)	\(16\)	\(16\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(961, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(961, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)