Space of modular forms of level 4050, weight 2, and Character 4050.c

• Label: 4050.2.c
• Level: $4050$
• Weight: $2$
• Character orbit: 4050.c
• Rep. character: $\chi_{4050}(649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $28$
• Sturm bound: $1620$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4050 = 2 \cdot 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4050.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(1620\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\), \(29\), \(41\), \(71\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4050, [\chi])\).

	Total	New	Old
Modular forms	882	72	810
Cusp forms	738	72	666
Eisenstein series	144	0	144

Trace form

\( 72 q - 72 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4050, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4050.2.c.a	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-6q^{11}+\cdots\)
4050.2.c.b	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-6q^{11}+\cdots\)
4050.2.c.c	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-3q^{11}+\cdots\)
4050.2.c.d	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-3q^{11}+\cdots\)
4050.2.c.e	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-3q^{11}+\cdots\)
4050.2.c.f	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+5iq^{7}-iq^{8}+iq^{13}+\cdots\)
4050.2.c.g	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-iq^{13}+\cdots\)
4050.2.c.h	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+4iq^{13}+\cdots\)
4050.2.c.i	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+5iq^{13}+\cdots\)
4050.2.c.j	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4iq^{13}+\cdots\)
4050.2.c.k	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+5iq^{13}+\cdots\)
4050.2.c.l	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-4iq^{13}+\cdots\)
4050.2.c.m	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+4iq^{13}+\cdots\)
4050.2.c.n	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-iq^{13}+\cdots\)
4050.2.c.o	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+5iq^{7}+iq^{8}+iq^{13}+\cdots\)
4050.2.c.p	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{11}+\cdots\)
4050.2.c.q	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{11}+\cdots\)
4050.2.c.r	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+3q^{11}+\cdots\)
4050.2.c.s	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+6q^{11}+\cdots\)
4050.2.c.t	$4050$	$2$	4050.c	5.b	$2$	$2$	$2$	$32.339$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+6q^{11}+\cdots\)
4050.2.c.u	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-q^{4}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.v	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}-\beta _{2}q^{8}+(-2+\cdots)q^{11}+\cdots\)
4050.2.c.w	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+(2\beta _{1}-\beta _{2})q^{7}-\beta _{1}q^{8}+\cdots\)
4050.2.c.x	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.y	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}+(2\beta _{1}-\beta _{2})q^{7}+\beta _{1}q^{8}+\cdots\)
4050.2.c.z	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2})q^{7}+\cdots\)
4050.2.c.ba	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+(2+\cdots)q^{11}+\cdots\)
4050.2.c.bb	$4050$	$2$	4050.c	5.b	$2$	$4$	$4$	$32.339$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-q^{4}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)