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

• Label: 245.2.t
• Level: $245$
• Weight: $2$
• Character orbit: 245.t
• Rep. character: $\chi_{245}(4,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $312$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.t (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	360	360	0
Cusp forms	312	312	0
Eisenstein series	48	48	0

Trace form

312 * q - 50 * q^4 - 12 * q^5 - 10 * q^6 - 64 * q^9 - 10 * q^10 - 40 * q^11 - 36 * q^14 - 6 * q^16 + 30 * q^19 - 46 * q^20 - 18 * q^21 - 34 * q^24 - 18 * q^25 - 10 * q^26 - 46 * q^29 + q^30 - 94 * q^31 + 64 * q^34 + 2 * q^35 - 46 * q^36 + 30 * q^39 + 26 * q^40 - 76 * q^41 + 8 * q^44 + 81 * q^45 - 114 * q^46 + 2 * q^49 + 86 * q^50 - 78 * q^51 + 4 * q^54 + 21 * q^55 - 118 * q^56 - 34 * q^59 + 70 * q^60 - 70 * q^61 - 32 * q^64 - 16 * q^65 + 70 * q^66 - 16 * q^69 + 80 * q^70 - 14 * q^71 - 26 * q^74 - 48 * q^75 - 158 * q^76 - 16 * q^79 + 12 * q^80 + 80 * q^81 + 132 * q^84 - 62 * q^85 - 102 * q^86 + 24 * q^89 + 222 * q^90 + 46 * q^91 - 98 * q^94 + 119 * q^95 + 144 * q^96 - 168 * q^99

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.t.a	$245$	$2$	245.t	245.t	$42$	$312$	$26$	$1.956$		None		✓	✓	✓	245.2.t.a	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$