Space of modular forms of level 5376, weight 2, and Character 5376.c

• Label: 5376.2.c
• Level: $5376$
• Weight: $2$
• Character orbit: 5376.c
• Rep. character: $\chi_{5376}(2689,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $40$
• Sturm bound: $2048$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 5376 = 2^{8} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5376.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 40 \)
Sturm bound:			\(2048\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\), \(71\), \(79\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5376, [\chi])\).

	Total	New	Old
Modular forms	1072	96	976
Cusp forms	976	96	880
Eisenstein series	96	0	96

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5376, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5376.2.c.a	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{5}-q^{7}-q^{9}-6iq^{11}+\cdots\)
5376.2.c.b	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{5}-q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.c	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.d	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.e	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.f	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.g	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.h	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{7}-q^{9}-2iq^{11}+4iq^{13}+\cdots\)
5376.2.c.i	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{7}-q^{9}+6iq^{11}+2iq^{13}+\cdots\)
5376.2.c.j	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
5376.2.c.k	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{7}-q^{9}+6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.l	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.m	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.n	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+2q^{15}+\cdots\)
5376.2.c.o	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.p	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.q	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.r	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.s	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.t	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2q^{15}+\cdots\)
5376.2.c.u	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.v	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.w	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-4iq^{13}+\cdots\)
5376.2.c.x	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+q^{7}-q^{9}+6iq^{11}-2iq^{13}+\cdots\)
5376.2.c.y	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
5376.2.c.z	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+q^{7}-q^{9}-6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.ba	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.bb	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.bc	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.bd	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.be	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{5}+q^{7}-q^{9}+6iq^{11}+\cdots\)
5376.2.c.bf	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+4iq^{5}+q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.bg	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bh	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)
5376.2.c.bi	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bj	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bk	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bl	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bm	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bn	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5376, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5376, [\chi]) \cong \)