Space of modular forms of level 1320, weight 2, and Character 1320.bw

• Label: 1320.2.bw
• Level: $1320$
• Weight: $2$
• Character orbit: 1320.bw
• Rep. character: $\chi_{1320}(361,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $96$
• Newform subspaces: $9$
• Sturm bound: $576$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(576\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

	Total	New	Old
Modular forms	1216	96	1120
Cusp forms	1088	96	992
Eisenstein series	128	0	128

Trace form

96 * q - 24 * q^9 + 4 * q^11 + 8 * q^13 - 24 * q^17 + 8 * q^19 - 32 * q^23 - 24 * q^25 - 24 * q^29 + 16 * q^31 + 8 * q^35 + 8 * q^37 + 8 * q^39 + 36 * q^41 + 96 * q^43 + 80 * q^47 + 36 * q^49 - 48 * q^53 - 16 * q^55 + 8 * q^57 - 40 * q^59 - 72 * q^61 - 24 * q^65 + 8 * q^69 + 8 * q^71 - 8 * q^73 + 120 * q^77 - 60 * q^79 - 24 * q^81 + 8 * q^85 + 120 * q^89 - 4 * q^91 + 16 * q^93 - 16 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1320.2.bw.a	$1320$	$2$	1320.bw	11.c	$5$	$4$	$1$	$10.540$	\(\Q(\zeta_{10})\)	None		✓			1320.2.bw.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
1320.2.bw.b	$1320$	$2$	1320.bw	11.c	$5$	$8$	$2$	$10.540$	8.0.13140625.1	None		✓			1320.2.bw.b	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{4}q^{3}-\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1320.2.bw.c	$1320$	$2$	1320.bw	11.c	$5$	$8$	$2$	$10.540$	8.0.159390625.1	None		✓			1320.2.bw.c	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{3}+\beta _{2}q^{5}+\cdots\)
1320.2.bw.d	$1320$	$2$	1320.bw	11.c	$5$	$12$	$3$	$10.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1320.2.bw.d	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{3}-\beta _{4}+\beta _{6})q^{3}+\beta _{6}q^{5}+\cdots\)
1320.2.bw.e	$1320$	$2$	1320.bw	11.c	$5$	$12$	$3$	$10.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1320.2.bw.e	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{3}-\beta _{2}q^{5}+(-1+\beta _{2}+\beta _{9}+\cdots)q^{7}+\cdots\)
1320.2.bw.f	$1320$	$2$	1320.bw	11.c	$5$	$12$	$3$	$10.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1320.2.bw.f	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{3}+(-1+\beta _{6}-\beta _{7}+\beta _{8})q^{5}+\cdots\)
1320.2.bw.g	$1320$	$2$	1320.bw	11.c	$5$	$12$	$3$	$10.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1320.2.bw.g	$2$	$0$	\(0\)	\(3\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{7}q^{3}+\beta _{8}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+\cdots\)
1320.2.bw.h	$1320$	$2$	1320.bw	11.c	$5$	$12$	$3$	$10.540$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1320.2.bw.h	$2$	$0$	\(0\)	\(3\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{7}q^{3}-\beta _{5}q^{5}+(1+\beta _{5}+\beta _{8})q^{7}+\cdots\)
1320.2.bw.i	$1320$	$2$	1320.bw	11.c	$5$	$16$	$4$	$10.540$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		1320.2.bw.i	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}-\beta _{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)