Space of modular forms of level 2250, weight 2, and Character 2250.c

• Label: 2250.2.c
• Level: $2250$
• Weight: $2$
• Character orbit: 2250.c
• Rep. character: $\chi_{2250}(1999,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $9$
• Sturm bound: $900$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2250 = 2 \cdot 3^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2250.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(900\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2250, [\chi])\).

	Total	New	Old
Modular forms	490	40	450
Cusp forms	410	40	370
Eisenstein series	80	0	80

Trace form

40 * q - 40 * q^4 - 2 * q^11 + 40 * q^16 - 34 * q^19 + 2 * q^26 + 2 * q^29 + 32 * q^31 + 4 * q^34 - 4 * q^41 + 2 * q^44 + 4 * q^46 - 76 * q^49 - 50 * q^59 + 34 * q^61 - 40 * q^64 + 8 * q^71 + 2 * q^74 + 34 * q^76 - 40 * q^79 + 54 * q^86 - 16 * q^89 + 80 * q^91 - 8 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(2250, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2250.2.c.a	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					250.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}+\beta _{1}q^{7}-\beta _{3}q^{8}+(-5+\cdots)q^{11}+\cdots\)
2250.2.c.b	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					750.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}+2\beta _{1}q^{7}+\beta _{3}q^{8}+(-2+\cdots)q^{11}+\cdots\)
2250.2.c.c	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None		✓			2250.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}-2\beta _{3}q^{7}-\beta _{3}q^{8}+(-1+\cdots)q^{11}+\cdots\)
2250.2.c.d	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					750.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}+\beta _{1}q^{7}-\beta _{3}q^{8}+(1+\cdots)q^{11}+\cdots\)
2250.2.c.e	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					750.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}+(2\beta _{1}-2\beta _{3})q^{7}-\beta _{3}q^{8}+\cdots\)
2250.2.c.f	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None		✓			2250.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}-2\beta _{3}q^{7}+\beta _{3}q^{8}+(1+\cdots)q^{11}+\cdots\)
2250.2.c.g	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					750.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}+(\beta _{1}+4\beta _{3})q^{7}-\beta _{3}q^{8}+\cdots\)
2250.2.c.h	$2250$	$2$	2250.c	5.b	$2$	$4$	$4$	$17.966$	\(\Q(i, \sqrt{5})\)	None					250.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}+(-3\beta _{1}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots\)
2250.2.c.i	$2250$	$2$	2250.c	5.b	$2$	$8$	$8$	$17.966$	8.0.9292960000.1	None		✓	✓		2250.2.a.q	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{3}q^{7}-\beta _{1}q^{8}+\beta _{7}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2250, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2250, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1125, [\chi])\)\(^{\oplus 2}\)