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

• Label: 650.2.o
• Level: $650$
• Weight: $2$
• Character orbit: 650.o
• Rep. character: $\chi_{650}(399,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $210$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(210\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	236	44	192
Cusp forms	188	44	144
Eisenstein series	48	0	48

Trace form

44 * q + 22 * q^4 + 34 * q^9 + 12 * q^11 - 24 * q^14 - 22 * q^16 + 16 * q^19 + 8 * q^21 - 14 * q^26 + 22 * q^29 + 32 * q^31 + 52 * q^34 - 34 * q^36 - 20 * q^39 + 10 * q^41 + 24 * q^44 + 14 * q^49 - 16 * q^51 - 12 * q^54 - 12 * q^56 - 20 * q^59 - 2 * q^61 - 44 * q^64 + 16 * q^66 - 36 * q^69 - 48 * q^71 - 6 * q^74 - 16 * q^76 - 56 * q^79 - 46 * q^81 + 4 * q^84 - 24 * q^86 + 20 * q^89 + 76 * q^91 + 28 * q^94 + 64 * 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.o.a	$650$	$2$	650.o	65.n	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					130.2.e.d	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2})q^{3}+\cdots\)
650.2.o.b	$650$	$2$	650.o	65.n	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					130.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-2\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}^{2}q^{6}+\cdots\)
650.2.o.c	$650$	$2$	650.o	65.n	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					26.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-4\zeta_{12}+4\zeta_{12}^{3})q^{7}+\cdots\)
650.2.o.d	$650$	$2$	650.o	65.n	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					130.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots\)
650.2.o.e	$650$	$2$	650.o	65.n	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					130.2.e.d	$2$	$0$	\(0\)	\(6\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(1+\zeta_{12}+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
650.2.o.f	$650$	$2$	650.o	65.n	$6$	$8$	$4$	$5.190$	8.0.49787136.1	None		✓			650.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{7})q^{3}+\cdots\)
650.2.o.g	$650$	$2$	650.o	65.n	$6$	$8$	$4$	$5.190$	8.0.3317760000.2	None					130.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{5}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
650.2.o.h	$650$	$2$	650.o	65.n	$6$	$8$	$4$	$5.190$	8.0.592240896.1	None		✓			650.2.e.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)

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

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