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

• Label: 961.2.g
• Level: $961$
• Weight: $2$
• Character orbit: 961.g
• Rep. character: $\chi_{961}(235,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $504$
• Newform subspaces: $23$
• Sturm bound: $165$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(165\)
Trace bound:			\(7\)
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	792	728	64
Cusp forms	536	504	32
Eisenstein series	256	224	32

Trace form

504 * q + 6 * q^2 + 12 * q^3 - 86 * q^4 + 3 * q^5 - 11 * q^6 - 2 * q^7 - 23 * q^8 + 45 * q^9 + 5 * q^10 + 7 * q^11 - 5 * q^12 + 7 * q^13 + 9 * q^14 - 14 * q^15 - 38 * q^16 + 6 * q^17 + 3 * q^18 - 16 * q^19 - 34 * q^20 - 9 * q^21 - 9 * q^22 - q^23 + 20 * q^24 - 7 * q^25 - 9 * q^26 - 9 * q^27 + 33 * q^28 + 14 * q^29 + 22 * q^30 - 150 * q^32 + 13 * q^33 + 32 * q^34 - 3 * q^35 + 39 * q^36 + 8 * q^37 - 5 * q^38 - 5 * q^39 + 7 * q^40 + 12 * q^41 - 69 * q^42 - 23 * q^43 - 39 * q^44 - 61 * q^45 - 34 * q^46 - 26 * q^47 - 34 * q^48 - 27 * q^49 + 46 * q^51 - 29 * q^52 - 6 * q^53 + 46 * q^54 + 7 * q^55 + 6 * q^56 + 17 * q^57 + 15 * q^58 + 75 * q^60 + 60 * q^61 - 130 * q^63 + 51 * q^64 + 12 * q^65 + 134 * q^66 - 37 * q^67 - 30 * q^68 - 34 * q^69 - 42 * q^70 + 22 * q^71 - 22 * q^72 - 2 * q^73 - 13 * q^74 - 13 * q^75 + 27 * q^76 - 18 * q^77 - q^78 - 18 * q^79 - 27 * q^80 - 74 * q^81 + q^82 + 16 * q^83 - 8 * q^84 - 37 * q^85 + 26 * q^86 - 47 * q^87 + 17 * q^88 - q^89 + 38 * q^90 - 8 * q^91 + 64 * q^92 - 252 * q^94 + 2 * q^95 - 8 * q^96 - 11 * q^97 - 34 * q^98 - 6 * 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.g.a	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.a.a	$4$	$0$	\(-6\)	\(-6\)	\(-4\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\zeta_{15}^{6})q^{2}+(-2+2\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
961.2.g.b	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.d.a	$4$	$0$	\(-6\)	\(-1\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\zeta_{15}^{6})q^{2}-\zeta_{15}^{7}q^{3}+(1-\zeta_{15}^{2}+\cdots)q^{4}+\cdots\)
961.2.g.c	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.d.a	$4$	$0$	\(-6\)	\(1\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\zeta_{15}^{6})q^{2}+\zeta_{15}^{7}q^{3}+(1-\zeta_{15}^{2}+\cdots)q^{4}+\cdots\)
961.2.g.d	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.a.a	$4$	$0$	\(-6\)	\(6\)	\(-4\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\zeta_{15}^{6})q^{2}+(2-2\zeta_{15}^{4}+2\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
961.2.g.e	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.a.a	$4$	$0$	\(4\)	\(-4\)	\(-4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1+\zeta_{15}^{3}+\zeta_{15}^{6})q^{2}+(-2+2\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
961.2.g.f	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.d.a	$4$	$0$	\(4\)	\(-1\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1+\zeta_{15}^{3}+\zeta_{15}^{6})q^{2}-\zeta_{15}^{7}q^{3}+\cdots\)
961.2.g.g	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.d.a	$4$	$0$	\(4\)	\(1\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1+\zeta_{15}^{3}+\zeta_{15}^{6})q^{2}+\zeta_{15}^{7}q^{3}+\cdots\)
961.2.g.h	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	\(\Q(\zeta_{15})\)	None					31.2.a.a	$4$	$0$	\(4\)	\(4\)	\(-4\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1+\zeta_{15}^{3}+\zeta_{15}^{6})q^{2}+(2-2\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
961.2.g.i	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	16.0.\(\cdots\).2	None		✓			961.2.a.h	$8$	$0$	\(-16\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-2\beta _{4}+\beta _{6}+\beta _{12}-2\beta _{13})q^{2}+\cdots\)
961.2.g.j	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(-6\)	\(-3\)	\(-3\)	\(-13\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
961.2.g.k	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(-6\)	\(3\)	\(-3\)	\(-13\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
961.2.g.l	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(-6\)	\(12\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
961.2.g.m	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(-3\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{2}-\beta _{3}-\beta _{9}-\beta _{10}+\beta _{12}+\beta _{13}+\cdots)q^{2}+\cdots\)
961.2.g.n	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(-3\)	\(-3\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{2}-\beta _{3}-\beta _{9}-\beta _{10}+\beta _{12}+\beta _{13}+\cdots)q^{2}+\cdots\)
961.2.g.o	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	16.0.\(\cdots\).2	None					31.2.c.a	$8$	$0$	\(4\)	\(-2\)	\(-8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\beta _{3}+\beta _{15})q^{2}+(\beta _{2}-\beta _{5}+\beta _{10}+\cdots)q^{3}+\cdots\)
961.2.g.p	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	16.0.\(\cdots\).2	None		✓			961.2.a.h	$8$	$0$	\(4\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\beta _{4}-\beta _{6}-\beta _{12}-\beta _{13})q^{2}+(\beta _{5}+\cdots)q^{3}+\cdots\)
961.2.g.q	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	16.0.\(\cdots\).2	None		✓			961.2.a.b	$16$	$0$	\(4\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1-\beta _{4}+\beta _{6}+\beta _{12}-\beta _{13})q^{2}+(-2\beta _{1}+\cdots)q^{3}+\cdots\)
961.2.g.r	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	16.0.\(\cdots\).2	None					31.2.c.a	$8$	$0$	\(4\)	\(2\)	\(-8\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1-\beta _{3}-\beta _{4}+\beta _{6}+\beta _{12}-\beta _{13}+\cdots)q^{2}+\cdots\)
961.2.g.s	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(3\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{2}-\beta _{3}-\beta _{9}-\beta _{10}+\beta _{12}+\beta _{13}+\cdots)q^{2}+\cdots\)
961.2.g.t	$961$	$2$	961.g	31.g	$15$	$16$	$2$	$7.674$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					31.2.g.a	$2$	$0$	\(4\)	\(3\)	\(-3\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(\beta _{2}-\beta _{3}-\beta _{9}-\beta _{10}+\beta _{12}+\beta _{13}+\cdots)q^{2}+\cdots\)
961.2.g.u	$961$	$2$	961.g	31.g	$15$	$24$	$3$	$7.674$		\(\Q(\sqrt{-31}) \)		✓			961.2.a.g	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{15}]$
961.2.g.v	$961$	$2$	961.g	31.g	$15$	$96$	$12$	$7.674$		None		✓			961.2.a.k	$16$	$0$	\(0\)	\(0\)	\(-32\)	\(8\)		$\mathrm{SU}(2)[C_{15}]$
961.2.g.w	$961$	$2$	961.g	31.g	$15$	$128$	$16$	$7.674$		None		✓	✓		961.2.a.l	$16$	$0$	\(16\)	\(0\)	\(64\)	\(-16\)		$\mathrm{SU}(2)[C_{15}]$

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

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