Space of modular forms of level 1650, weight 2, and Character 1650.c

• Label: 1650.2.c
• Level: $1650$
• Weight: $2$
• Character orbit: 1650.c
• Rep. character: $\chi_{1650}(199,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $15$
• Sturm bound: $720$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(720\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).

	Total	New	Old
Modular forms	384	32	352
Cusp forms	336	32	304
Eisenstein series	48	0	48

Trace form

32 * q - 32 * q^4 - 32 * q^9 + 32 * q^16 - 8 * q^19 + 8 * q^21 + 24 * q^26 - 24 * q^29 - 24 * q^31 - 40 * q^34 + 32 * q^36 - 8 * q^39 - 8 * q^41 - 24 * q^49 + 32 * q^59 - 32 * q^64 + 8 * q^66 - 16 * q^69 - 96 * q^71 - 24 * q^74 + 8 * q^76 - 8 * q^79 + 32 * q^81 - 8 * q^84 - 32 * q^86 + 24 * q^89 + 32 * q^91 - 32 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1650.2.c.a	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					330.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
1650.2.c.b	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
1650.2.c.c	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
1650.2.c.d	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					66.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
1650.2.c.e	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					66.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
1650.2.c.f	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\)
1650.2.c.g	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					330.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-i q^{8}+\cdots\)
1650.2.c.h	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
1650.2.c.i	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					330.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+i q^{8}+\cdots\)
1650.2.c.j	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					330.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+4 i q^{7}+\cdots\)
1650.2.c.k	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+3 i q^{7}+\cdots\)
1650.2.c.l	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					330.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{8}+\cdots\)
1650.2.c.m	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None					66.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
1650.2.c.n	$1650$	$2$	1650.c	5.b	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-1}) \)	None		✓			1650.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
1650.2.c.o	$1650$	$2$	1650.c	5.b	$2$	$4$	$4$	$13.175$	\(\Q(i, \sqrt{73})\)	None		✓	✓		1650.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)