Space of modular forms of level 245, weight 2, and Character 245.l

• Label: 245.2.l
• Level: $245$
• Weight: $2$
• Character orbit: 245.l
• Rep. character: $\chi_{245}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $56$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(56\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

	Total	New	Old
Modular forms	144	96	48
Cusp forms	80	64	16
Eisenstein series	64	32	32

Trace form

64 * q + 2 * q^2 + 6 * q^3 - 20 * q^8 - 6 * q^10 - 8 * q^11 - 6 * q^12 - 12 * q^15 + 4 * q^16 - 12 * q^17 - 36 * q^18 - 48 * q^22 - 14 * q^23 + 20 * q^25 + 24 * q^26 - 20 * q^30 + 24 * q^31 + 62 * q^32 + 56 * q^36 - 8 * q^37 + 12 * q^38 - 18 * q^40 - 4 * q^43 - 24 * q^45 - 52 * q^46 - 24 * q^47 - 92 * q^50 + 20 * q^51 - 24 * q^52 + 24 * q^53 - 72 * q^57 + 70 * q^58 + 10 * q^60 + 24 * q^61 + 40 * q^65 + 12 * q^66 + 22 * q^67 + 12 * q^68 - 88 * q^71 - 8 * q^72 + 24 * q^73 + 6 * q^75 + 120 * q^78 + 24 * q^80 - 60 * q^81 + 6 * q^82 - 32 * q^85 - 52 * q^86 - 18 * q^87 - 16 * q^88 + 28 * q^92 - 48 * q^93 + 60 * q^95 - 60 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.2.l.a	$245$	$2$	245.l	35.k	$12$	$4$	$1$	$1.956$	\(\Q(\zeta_{12})\)	None					35.2.k.a	$2$	$0$	\(-4\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
245.2.l.b	$245$	$2$	245.l	35.k	$12$	$4$	$1$	$1.956$	\(\Q(\zeta_{12})\)	None					35.2.k.a	$2$	$0$	\(2\)	\(4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
245.2.l.c	$245$	$2$	245.l	35.k	$12$	$8$	$2$	$1.956$	8.0.3317760000.2	None					35.2.f.a	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{5}+\cdots\)
245.2.l.d	$245$	$2$	245.l	35.k	$12$	$48$	$12$	$1.956$		None		✓	✓		245.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)