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

• Label: 1650.2.d
• Level: $1650$
• Weight: $2$
• Character orbit: 1650.d
• Rep. character: $\chi_{1650}(1451,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $10$
• Sturm bound: $720$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(720\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\), \(17\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	384	76	308
Cusp forms	336	76	260
Eisenstein series	48	0	48

Trace form

76 * q + 76 * q^4 + 8 * q^9 + 76 * q^16 + 24 * q^27 + 32 * q^31 - 24 * q^33 - 16 * q^34 + 8 * q^36 + 16 * q^37 - 8 * q^42 - 28 * q^49 + 32 * q^58 + 76 * q^64 + 18 * q^66 + 40 * q^67 - 64 * q^69 + 40 * q^78 + 72 * q^81 + 8 * q^82 - 40 * q^91 - 32 * q^93 - 16 * q^97 - 2 * q^99

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.d.a	$1650$	$2$	1650.d	33.d	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-2}) \)	None					66.2.b.a	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1650.2.d.b	$1650$	$2$	1650.d	33.d	$2$	$2$	$2$	$13.175$	\(\Q(\sqrt{-2}) \)	None					66.2.b.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1650.2.d.c	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.2051727616.3	None					330.2.d.a	$2$	$0$	\(-8\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1650.2.d.d	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.\(\cdots\).1	None		✓			1650.2.d.d	$2$	$0$	\(-8\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.e	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.\(\cdots\).1	None		✓			1650.2.d.d	$2$	$0$	\(-8\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.f	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.2051727616.3	None					330.2.d.a	$2$	$0$	\(8\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-\beta _{3}-\beta _{4})q^{3}+q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1650.2.d.g	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.\(\cdots\).1	None		✓			1650.2.d.d	$2$	$0$	\(8\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.h	$1650$	$2$	1650.d	33.d	$2$	$8$	$8$	$13.175$	8.0.\(\cdots\).1	None		✓			1650.2.d.d	$2$	$0$	\(8\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.i	$1650$	$2$	1650.d	33.d	$2$	$12$	$12$	$13.175$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					330.2.f.a	$4$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
1650.2.d.j	$1650$	$2$	1650.d	33.d	$2$	$12$	$12$	$13.175$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					330.2.f.a	$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{7}q^{3}+q^{4}-\beta _{7}q^{6}-\beta _{2}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)