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

• Label: 245.2.p
• Level: $245$
• Weight: $2$
• Character orbit: 245.p
• Rep. character: $\chi_{245}(29,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $156$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.p (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	180	180	0
Cusp forms	156	156	0
Eisenstein series	24	24	0

Trace form

156 * q + 14 * q^4 - 3 * q^5 - 32 * q^6 + 22 * q^9 - 11 * q^10 + 4 * q^11 - 18 * q^14 - 15 * q^15 - 30 * q^16 - 84 * q^19 + 13 * q^20 - 12 * q^21 - 14 * q^24 - 15 * q^25 - 32 * q^26 + 16 * q^29 - 16 * q^30 + 52 * q^31 - 70 * q^34 - 5 * q^35 - 32 * q^36 + 18 * q^39 + 91 * q^40 - 32 * q^41 + 64 * q^44 + 15 * q^45 - 84 * q^46 + 16 * q^49 - 122 * q^50 - 66 * q^51 + 50 * q^54 + 51 * q^55 - 56 * q^56 + 34 * q^59 + 35 * q^60 - 26 * q^61 + 38 * q^64 - 11 * q^65 - 100 * q^66 - 2 * q^69 - 83 * q^70 - 16 * q^71 + 8 * q^74 + 27 * q^75 + 140 * q^76 - 32 * q^79 + 12 * q^80 - 122 * q^81 - 186 * q^84 + 47 * q^85 + 90 * q^86 - 84 * q^89 + 132 * q^90 - 82 * q^91 + 44 * q^94 + 16 * q^95 - 96 * q^96 + 96 * 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.p.a	$245$	$2$	245.p	245.p	$14$	$12$	$2$	$1.956$	\(\Q(\zeta_{28})\)	None		✓			245.2.p.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}+(-2\zeta_{28}^{3}+\zeta_{28}^{5}-\zeta_{28}^{7}+\cdots)q^{3}+\cdots\)
245.2.p.b	$245$	$2$	245.p	245.p	$14$	$144$	$24$	$1.956$		None		✓	✓		245.2.p.b	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$