Space of modular forms of level 960, weight 3, and Character 960.c

• Label: 960.3.c
• Level: $960$
• Weight: $3$
• Character orbit: 960.c
• Rep. character: $\chi_{960}(449,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $13$
• Sturm bound: $576$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(576\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(960, [\chi])\).

	Total	New	Old
Modular forms	408	100	308
Cusp forms	360	92	268
Eisenstein series	48	8	40

Trace form

\( 92 q - 4 q^{9} - 32 q^{21} - 4 q^{25} - 96 q^{45} - 484 q^{49} + 40 q^{61} - 440 q^{69} - 36 q^{81} + 104 q^{85}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(960, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
960.3.c.a	$960$	$3$	960.c	15.d	$2$	$1$	$1$	$26.158$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}-5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots\)
960.3.c.b	$960$	$3$	960.c	15.d	$2$	$1$	$1$	$26.158$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(-3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+5q^{5}+9q^{9}-15q^{15}+14q^{17}+\cdots\)
960.3.c.c	$960$	$3$	960.c	15.d	$2$	$1$	$1$	$26.158$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}-5q^{5}+9q^{9}-15q^{15}-14q^{17}+\cdots\)
960.3.c.d	$960$	$3$	960.c	15.d	$2$	$1$	$1$	$26.158$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots\)
960.3.c.e	$960$	$3$	960.c	15.d	$2$	$4$	$4$	$26.158$	\(\Q(\sqrt{2}, \sqrt{-17})\)	None					30.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
960.3.c.f	$960$	$3$	960.c	15.d	$2$	$4$	$4$	$26.158$	\(\Q(\sqrt{2}, \sqrt{-17})\)	None					30.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
960.3.c.g	$960$	$3$	960.c	15.d	$2$	$4$	$4$	$26.158$	\(\Q(i, \sqrt{5})\)	None					60.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.c.h	$960$	$3$	960.c	15.d	$2$	$4$	$4$	$26.158$	\(\Q(i, \sqrt{5})\)	None					60.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
960.3.c.i	$960$	$3$	960.c	15.d	$2$	$8$	$8$	$26.158$	8.0.40960000.1	\(\Q(\sqrt{-5}) \)					480.3.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{3}+5\beta _{1}q^{5}+(2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.c.j	$960$	$3$	960.c	15.d	$2$	$12$	$12$	$26.158$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					120.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
960.3.c.k	$960$	$3$	960.c	15.d	$2$	$12$	$12$	$26.158$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					120.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
960.3.c.l	$960$	$3$	960.c	15.d	$2$	$16$	$16$	$26.158$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					480.3.c.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{7}+\beta _{10})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
960.3.c.m	$960$	$3$	960.c	15.d	$2$	$24$	$24$	$26.158$		None			✓		480.3.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(960, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)