Space of modular forms of level 2880, weight 2, and Character 2880.w

• Label: 2880.2.w
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.w
• Rep. character: $\chi_{2880}(2177,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $17$
• Sturm bound: $1152$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1152\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

	Total	New	Old
Modular forms	1248	96	1152
Cusp forms	1056	96	960
Eisenstein series	192	0	192

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.2.w.a	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2})q^{7}+\cdots\)
2880.2.w.b	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
2880.2.w.c	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
2880.2.w.d	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-5+5\zeta_{8}^{2})q^{13}+\cdots\)
2880.2.w.e	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
2880.2.w.f	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-4\zeta_{8}-4\zeta_{8}^{3})q^{11}+\cdots\)
2880.2.w.g	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(-1-\zeta_{8}^{2})q^{13}+\cdots\)
2880.2.w.h	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(1+\zeta_{8}^{2})q^{13}-8\zeta_{8}q^{17}+\cdots\)
2880.2.w.i	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+(5+5\zeta_{8}^{2})q^{13}+\cdots\)
2880.2.w.j	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
2880.2.w.k	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
2880.2.w.l	$2880$	$2$	2880.w	15.e	$4$	$4$	$2$	$22.997$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
2880.2.w.m	$2880$	$2$	2880.w	15.e	$4$	$8$	$4$	$22.997$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{5}+(-1+\beta _{2}+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2880.2.w.n	$2880$	$2$	2880.w	15.e	$4$	$8$	$4$	$22.997$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{24}+2\zeta_{24}^{3})q^{5}+\zeta_{24}^{5}q^{7}+\zeta_{24}^{7}q^{11}+\cdots\)
2880.2.w.o	$2880$	$2$	2880.w	15.e	$4$	$8$	$4$	$22.997$	8.0.40960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{5}+(1-\beta _{2}-\beta _{3})q^{7}+(\beta _{1}+\beta _{6}+\cdots)q^{11}+\cdots\)
2880.2.w.p	$2880$	$2$	2880.w	15.e	$4$	$12$	$6$	$22.997$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+(\beta _{6}+\cdots)q^{11}+\cdots\)
2880.2.w.q	$2880$	$2$	2880.w	15.e	$4$	$12$	$6$	$22.997$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(\beta _{6}+\beta _{8}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)