Space of modular forms of level 676, weight 3, and Character 676.p

• Label: 676.3.p
• Level: $676$
• Weight: $3$
• Character orbit: 676.p
• Rep. character: $\chi_{676}(51,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $2160$
• Sturm bound: $273$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	676.p (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 676 \)
Character field:			\(\Q(\zeta_{26})\)
Sturm bound:			\(273\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(676, [\chi])\).

	Total	New	Old
Modular forms	2208	2208	0
Cusp forms	2160	2160	0
Eisenstein series	48	48	0

Trace form

2160 * q - 13 * q^2 - 11 * q^4 - 26 * q^5 - 13 * q^6 - 13 * q^8 + 506 * q^9 - 19 * q^10 - 59 * q^12 - 126 * q^13 - 11 * q^14 + 13 * q^16 - 42 * q^17 + 260 * q^18 - 13 * q^20 - 26 * q^21 + 26 * q^22 - 13 * q^24 + 778 * q^25 - 27 * q^26 - 13 * q^28 - 2 * q^29 - 151 * q^30 - 338 * q^32 - 26 * q^33 + 182 * q^34 + 49 * q^36 - 26 * q^37 - 390 * q^38 - 131 * q^40 - 26 * q^41 + 257 * q^42 - 13 * q^44 - 26 * q^45 + 39 * q^46 + 326 * q^48 - 1414 * q^49 - 13 * q^50 - 458 * q^52 - 176 * q^53 - 13 * q^54 + 391 * q^56 - 260 * q^57 - 13 * q^58 - 13 * q^60 - 234 * q^61 - 774 * q^62 - 101 * q^64 - 82 * q^65 - 1810 * q^66 + 1048 * q^68 + 208 * q^69 + 832 * q^72 - 26 * q^73 + 211 * q^74 - 1365 * q^76 + 270 * q^77 - 845 * q^78 - 1694 * q^81 - 77 * q^82 + 1222 * q^84 + 884 * q^85 - 13 * q^86 + 51 * q^88 + 255 * q^90 - 473 * q^92 - 962 * q^93 + 1155 * q^94 + 1846 * q^96 - 26 * q^97 - 13 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(676, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.