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	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

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