Space of modular forms of level 4650, weight 2, and Character 4650.d

• Label: 4650.2.d
• Level: $4650$
• Weight: $2$
• Character orbit: 4650.d
• Rep. character: $\chi_{4650}(3349,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $36$
• Sturm bound: $1920$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4650.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 36 \)
Sturm bound:			\(1920\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4650, [\chi])\).

	Total	New	Old
Modular forms	984	92	892
Cusp forms	936	92	844
Eisenstein series	48	0	48

Trace form

\( 92 q - 92 q^{4} - 92 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4650, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4650.2.d.a	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
4650.2.d.b	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.c	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
4650.2.d.d	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.e	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.f	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.s	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
4650.2.d.g	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.k	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.h	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
4650.2.d.i	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.j	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
4650.2.d.k	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					186.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
4650.2.d.l	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
4650.2.d.m	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
4650.2.d.n	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
4650.2.d.o	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
4650.2.d.p	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.q	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.r	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					186.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.s	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots\)
4650.2.d.t	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.u	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.n	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.v	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
4650.2.d.w	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.x	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.y	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.z	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					186.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
4650.2.d.ba	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None					930.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
4650.2.d.bb	$4650$	$2$	4650.d	5.b	$2$	$2$	$2$	$37.130$	\(\Q(\sqrt{-1}) \)	None		✓			4650.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
4650.2.d.bc	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{17})\)	None					186.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+2\beta _{1}q^{7}+\cdots\)
4650.2.d.bd	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{17})\)	None					930.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.be	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{5})\)	None		✓			4650.2.a.ca	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4650.2.d.bf	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{13})\)	None		✓			4650.2.a.cb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}-3\beta _{1}q^{7}+\cdots\)
4650.2.d.bg	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{65})\)	None					930.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.bh	$4650$	$2$	4650.d	5.b	$2$	$4$	$4$	$37.130$	\(\Q(i, \sqrt{33})\)	None					930.2.a.r	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
4650.2.d.bi	$4650$	$2$	4650.d	5.b	$2$	$6$	$6$	$37.130$	6.0.44836416.1	None		✓			4650.2.a.cj	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-q^{6}-\beta _{4}q^{7}+\cdots\)
4650.2.d.bj	$4650$	$2$	4650.d	5.b	$2$	$6$	$6$	$37.130$	6.0.120648256.1	None		✓			4650.2.a.cl	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+(\beta _{2}+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2325, [\chi])\)\(^{\oplus 2}\)