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

• Label: 650.2.l
• Level: $650$
• Weight: $2$
• Character orbit: 650.l
• Rep. character: $\chi_{650}(131,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $120$
• Newform subspaces: $5$
• Sturm bound: $210$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(210\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	432	120	312
Cusp forms	400	120	280
Eisenstein series	32	0	32

Trace form

120 * q + 8 * q^3 - 30 * q^4 - 12 * q^5 + 4 * q^6 + 16 * q^7 - 22 * q^9 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 24 * q^15 - 30 * q^16 + 12 * q^17 + 4 * q^19 + 8 * q^20 + 32 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 28 * q^25 - 24 * q^26 - 52 * q^27 - 4 * q^28 - 12 * q^29 - 26 * q^30 + 12 * q^31 + 16 * q^33 + 8 * q^34 + 18 * q^35 - 22 * q^36 + 40 * q^37 + 16 * q^38 + 4 * q^40 + 16 * q^41 + 32 * q^42 - 16 * q^43 + 12 * q^44 - 12 * q^45 - 16 * q^46 - 8 * q^47 - 12 * q^48 + 168 * q^49 + 32 * q^50 + 12 * q^51 - 4 * q^53 + 16 * q^54 + 40 * q^55 - 56 * q^57 + 32 * q^58 - 24 * q^59 - 16 * q^60 - 40 * q^61 - 2 * q^62 - 4 * q^63 - 30 * q^64 + 4 * q^65 + 32 * q^66 - 84 * q^67 - 88 * q^68 - 52 * q^69 - 44 * q^70 - 20 * q^71 - 6 * q^75 - 16 * q^76 - 8 * q^79 + 8 * q^80 + 6 * q^81 + 16 * q^82 - 32 * q^83 - 28 * q^84 - 96 * q^85 + 20 * q^86 + 4 * q^87 + 4 * q^88 + 88 * q^89 - 68 * q^90 + 4 * q^91 + 4 * q^92 + 56 * q^93 + 84 * q^95 + 4 * q^96 + 8 * q^97 + 64 * q^98 + 96 * 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.l.a	$650$	$2$	650.l	25.d	$5$	$4$	$1$	$5.190$	\(\Q(\zeta_{10})\)	None		✓			650.2.l.a	$2$	$0$	\(1\)	\(5\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
650.2.l.b	$650$	$2$	650.l	25.d	$5$	$20$	$5$	$5.190$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			650.2.l.b	$2$	$0$	\(5\)	\(-4\)	\(-10\)	\(8\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{10}q^{2}-\beta _{2}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots\)
650.2.l.c	$650$	$2$	650.l	25.d	$5$	$24$	$6$	$5.190$		None		✓			650.2.l.c	$2$	$0$	\(-6\)	\(3\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$
650.2.l.d	$650$	$2$	650.l	25.d	$5$	$36$	$9$	$5.190$		None		✓			650.2.l.d	$2$	$0$	\(-9\)	\(3\)	\(-3\)	\(8\)		$\mathrm{SU}(2)[C_{5}]$
650.2.l.e	$650$	$2$	650.l	25.d	$5$	$36$	$9$	$5.190$		None		✓			650.2.l.e	$2$	$0$	\(9\)	\(1\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{5}]$

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

\( S_{2}^{\mathrm{old}}(650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)