Space of modular forms of level 4950, weight 2, and Character 4950.c

• Label: 4950.2.c
• Level: $4950$
• Weight: $2$
• Character orbit: 4950.c
• Rep. character: $\chi_{4950}(199,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $31$
• Sturm bound: $2160$
• Trace bound: $26$

Defining parameters

Level:	\( N \)	\(=\)	\( 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4950.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(2160\)
Trace bound:			\(26\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4950, [\chi])\).

	Total	New	Old
Modular forms	1128	74	1054
Cusp forms	1032	74	958
Eisenstein series	96	0	96

Trace form

\( 74 q - 74 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4950, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4950.2.c.a	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+5iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.b	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.c	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.d	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.e	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.f	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.g	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}-q^{11}-2iq^{13}+\cdots\)
4950.2.c.h	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{8}-q^{11}+q^{16}+\cdots\)
4950.2.c.i	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}-q^{11}+3iq^{13}+\cdots\)
4950.2.c.j	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{8}-q^{11}-6iq^{13}+\cdots\)
4950.2.c.k	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.l	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.m	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.n	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.o	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.p	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.q	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.r	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.s	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.t	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.u	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{8}+q^{11}+q^{16}+\cdots\)
4950.2.c.v	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}+q^{11}-2iq^{13}+\cdots\)
4950.2.c.w	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.x	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.y	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.z	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.ba	$4950$	$2$	4950.c	5.b	$2$	$2$	$2$	$39.526$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.bb	$4950$	$2$	4950.c	5.b	$2$	$4$	$4$	$39.526$	\(\Q(i, \sqrt{73})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+q^{11}+\cdots\)
4950.2.c.bc	$4950$	$2$	4950.c	5.b	$2$	$4$	$4$	$39.526$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+q^{11}+\cdots\)
4950.2.c.bd	$4950$	$2$	4950.c	5.b	$2$	$6$	$6$	$39.526$	6.0.270273600.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+\beta _{3}q^{7}-\beta _{1}q^{8}-q^{11}+\cdots\)
4950.2.c.be	$4950$	$2$	4950.c	5.b	$2$	$6$	$6$	$39.526$	6.0.270273600.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}+\beta _{3}q^{7}+\beta _{1}q^{8}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)