Space of modular forms of level 650, weight 2, and Character 650.b

• Label: 650.2.b
• Level: $650$
• Weight: $2$
• Character orbit: 650.b
• Rep. character: $\chi_{650}(599,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $9$
• Sturm bound: $210$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(210\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

	Total	New	Old
Modular forms	118	18	100
Cusp forms	94	18	76
Eisenstein series	24	0	24

Trace form

18 * q - 18 * q^4 + 4 * q^6 - 18 * q^9 - 12 * q^11 - 8 * q^14 + 18 * q^16 + 4 * q^19 - 16 * q^21 - 4 * q^24 - 6 * q^26 - 16 * q^29 - 16 * q^31 + 8 * q^34 + 18 * q^36 + 8 * q^41 + 12 * q^44 - 26 * q^49 - 8 * q^51 - 4 * q^54 + 8 * q^56 + 32 * q^59 - 18 * q^64 - 28 * q^66 - 48 * q^71 - 32 * q^74 - 4 * q^76 + 40 * q^79 - 30 * q^81 + 16 * q^84 + 8 * q^86 + 64 * q^89 + 12 * q^91 - 40 * q^94 + 4 * q^96 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.b.a	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None					26.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}+i q^{7}+\cdots\)
650.2.b.b	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		✓			650.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+5 i q^{7}+\cdots\)
650.2.b.c	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		✓			650.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-4 i q^{7}+\cdots\)
650.2.b.d	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None					26.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
650.2.b.e	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None					130.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-i q^{8}+3 q^{9}-i q^{13}+\cdots\)
650.2.b.f	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None					130.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}+4 i q^{7}+\cdots\)
650.2.b.g	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None					130.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}-4 i q^{7}+\cdots\)
650.2.b.h	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		✓			650.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}+i q^{7}+\cdots\)
650.2.b.i	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		✓			650.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-3 i q^{3}-q^{4}+3 q^{6}-i q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)