Space of modular forms of level 676, weight 2, and Character 676.w

• Label: 676.2.w
• Level: $676$
• Weight: $2$
• Character orbit: 676.w
• Rep. character: $\chi_{676}(7,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $4272$
• Newform subspaces: $2$
• Sturm bound: $182$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.w (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 676 \)
Character field:			\(\Q(\zeta_{156})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(182\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(676, [\chi])\).

	Total	New	Old
Modular forms	4464	4464	0
Cusp forms	4272	4272	0
Eisenstein series	192	192	0

Trace form

4272 * q - 48 * q^2 - 46 * q^4 - 98 * q^5 - 38 * q^6 - 54 * q^8 - 270 * q^9 - 46 * q^10 - 52 * q^12 - 96 * q^13 - 60 * q^14 - 50 * q^16 - 92 * q^17 - 58 * q^18 - 66 * q^20 - 76 * q^21 - 34 * q^22 - 62 * q^24 - 104 * q^25 - 78 * q^26 - 64 * q^28 - 100 * q^29 - 94 * q^30 + 42 * q^32 - 84 * q^33 - 62 * q^34 - 46 * q^36 - 114 * q^37 - 182 * q^38 - 4 * q^40 - 124 * q^41 - 44 * q^42 - 44 * q^44 - 124 * q^45 + 46 * q^46 - 22 * q^48 - 164 * q^49 - 46 * q^50 + 134 * q^52 - 110 * q^53 - 36 * q^54 + 8 * q^56 - 116 * q^57 + 22 * q^58 - 28 * q^60 - 110 * q^61 - 164 * q^62 - 52 * q^64 - 108 * q^65 - 162 * q^66 - 60 * q^68 + 64 * q^69 - 80 * q^70 - 120 * q^72 - 146 * q^73 - 78 * q^74 - 74 * q^76 - 104 * q^77 + 140 * q^78 - 120 * q^80 + 34 * q^81 + 154 * q^82 - 136 * q^84 - 82 * q^85 - 68 * q^86 - 88 * q^88 - 46 * q^89 - 52 * q^90 + 80 * q^92 - 12 * q^93 - 202 * q^94 - 318 * q^96 - 66 * q^97 - 36 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(676, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
676.2.w.a	$676$	$2$	676.w	676.w	$156$	$48$	$1$	$5.398$		\(\Q(\sqrt{-1}) \)		✓			676.2.w.a	$4$	$0$	\(2\)	\(0\)	\(-6\)	\(0\)		$\mathrm{U}(1)[D_{156}]$
676.2.w.b	$676$	$2$	676.w	676.w	$156$	$4224$	$88$	$5.398$		None		✓	✓		676.2.w.b	$4$	$0$	\(-50\)	\(0\)	\(-92\)	\(0\)		$\mathrm{SU}(2)[C_{156}]$