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

$96 q - 96 q^{9} - 96 q^{25} + 96 q^{49} + 64 q^{65} - 64 q^{73} + 96 q^{81} - 64 q^{89}+O(q^{100})$

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5376.2.c.a	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{5}-q^{7}-q^{9}-6 i q^{11}+\cdots$
5376.2.c.b	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{5}-q^{7}-q^{9}+2 i q^{11}+\cdots$
5376.2.c.c	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}-q^{7}-q^{9}+4 i q^{11}+\cdots$
5376.2.c.d	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					168.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}-q^{7}-q^{9}-6 i q^{13}+\cdots$
5376.2.c.e	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					42.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}-q^{7}-q^{9}-4 i q^{11}+\cdots$
5376.2.c.f	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					168.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}-q^{7}-q^{9}+2 i q^{13}+\cdots$
5376.2.c.g	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.e	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-q^{7}-q^{9}-2 i q^{11}-6 q^{17}+\cdots$
5376.2.c.h	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.d	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-q^{7}-q^{9}-2 i q^{11}+4 i q^{13}+\cdots$
5376.2.c.i	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					84.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{7}-q^{9}+6 i q^{11}+2 i q^{13}+\cdots$
5376.2.c.j	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.c	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{7}-q^{9}-2 i q^{11}-2 i q^{13}+\cdots$
5376.2.c.k	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.f	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-q^{7}-q^{9}+6 i q^{11}-4 i q^{13}+\cdots$
5376.2.c.l	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					21.2.a.a	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}-q^{7}-q^{9}+4 i q^{11}+\cdots$
5376.2.c.m	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.b	$2$	$1$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}-q^{7}-q^{9}-4 i q^{11}+\cdots$
5376.2.c.n	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.c	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}-q^{7}-q^{9}+2 q^{15}+\cdots$
5376.2.c.o	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.d	$2$	$0$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}-q^{7}-q^{9}-2 i q^{13}+\cdots$
5376.2.c.p	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					84.2.a.a	$2$	$1$	$0$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{5}-q^{7}-q^{9}-2 i q^{11}+\cdots$
5376.2.c.q	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					84.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{5}+q^{7}-q^{9}+2 i q^{11}+\cdots$
5376.2.c.r	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					21.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}+q^{7}-q^{9}-4 i q^{11}+\cdots$
5376.2.c.s	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.b	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}+q^{7}-q^{9}+4 i q^{11}+\cdots$
5376.2.c.t	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.c	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}+q^{7}-q^{9}-2 q^{15}+\cdots$
5376.2.c.u	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.d	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}+q^{7}-q^{9}-2 i q^{13}+\cdots$
5376.2.c.v	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.e	$2$	$1$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+q^{7}-q^{9}-2 i q^{11}-6 q^{17}+\cdots$
5376.2.c.w	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.d	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+q^{7}-q^{9}-2 i q^{11}-4 i q^{13}+\cdots$
5376.2.c.x	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					84.2.a.b	$2$	$1$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+q^{7}-q^{9}+6 i q^{11}-2 i q^{13}+\cdots$
5376.2.c.y	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.c	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+q^{7}-q^{9}-2 i q^{11}+2 i q^{13}+\cdots$
5376.2.c.z	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.f	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+q^{7}-q^{9}-6 i q^{11}-4 i q^{13}+\cdots$
5376.2.c.ba	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.b	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}+q^{7}-q^{9}-4 i q^{11}+\cdots$
5376.2.c.bb	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					168.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}+q^{7}-q^{9}-6 i q^{13}+\cdots$
5376.2.c.bc	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					42.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}+q^{7}-q^{9}+4 i q^{11}+\cdots$
5376.2.c.bd	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					168.2.a.b	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+2 i q^{5}+q^{7}-q^{9}+2 i q^{13}+\cdots$
5376.2.c.be	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					2688.2.a.a	$2$	$1$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{5}+q^{7}-q^{9}+6 i q^{11}+\cdots$
5376.2.c.bf	$5376$	$2$	5376.c	8.b	$2$	$2$	$2$	$42.928$	$\Q(\sqrt{-1})$	None					672.2.a.a	$2$	$0$	$0$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+4 i q^{5}+q^{7}-q^{9}-2 i q^{11}+\cdots$
5376.2.c.bg	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(\zeta_{8})$	None					2688.2.a.ba	$2$	$0$	$0$	$0$	$0$	$-4$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+\beta_{2} q^{5}-q^{7}-q^{9}+(\beta_{2}+2\beta_1)q^{11}+\cdots$
5376.2.c.bh	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(\zeta_{12})$	None					672.2.a.i	$2$	$0$	$0$	$0$	$0$	$-4$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{2} q^{5}-q^{7}-q^{9}+(-\beta_{2}-2\beta_1)q^{11}+\cdots$
5376.2.c.bi	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(i, \sqrt{5})$	None					2688.2.a.y	$2$	$0$	$0$	$0$	$0$	$-4$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$
5376.2.c.bj	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(i, \sqrt{5})$	None					2688.2.a.z	$2$	$0$	$0$	$0$	$0$	$-4$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$
5376.2.c.bk	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(i, \sqrt{5})$	None					2688.2.a.y	$2$	$0$	$0$	$0$	$0$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$
5376.2.c.bl	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(i, \sqrt{5})$	None					2688.2.a.z	$2$	$0$	$0$	$0$	$0$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$
5376.2.c.bm	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(\zeta_{8})$	None					2688.2.a.ba	$2$	$0$	$0$	$0$	$0$	$4$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+\beta_{2} q^{5}+q^{7}-q^{9}+(-\beta_{2}-2\beta_1)q^{11}+\cdots$
5376.2.c.bn	$5376$	$2$	5376.c	8.b	$2$	$4$	$4$	$42.928$	$\Q(\zeta_{12})$	None					672.2.a.i	$2$	$0$	$0$	$0$	$0$	$4$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}-\beta_{2} q^{5}+q^{7}-q^{9}+(\beta_{2}-2\beta_1)q^{11}+\cdots$

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

$S_{2}^{\mathrm{old}}(5376, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(24, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(56, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(64, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(96, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(128, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(168, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(192, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(224, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(256, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(384, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(448, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(672, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(768, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(896, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1344, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1792, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(2688, [\chi])$$^{\oplus 2}$