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Properties

Label 676.6.m
Level $676$
Weight $6$
Character orbit 676.m
Rep. character $\chi_{676}(53,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $924$
Sturm bound $546$

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Defining parameters

Level: \( N \) \(=\) \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 676.m (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(676, [\chi])\).

Total New Old
Modular forms 5496 924 4572
Cusp forms 5424 924 4500
Eisenstein series 72 0 72

Trace form

\( 924 q - 22 q^{5} + 218 q^{7} - 6341 q^{9} + O(q^{10}) \) \( 924 q - 22 q^{5} + 218 q^{7} - 6341 q^{9} - 222 q^{11} + 1120 q^{13} + 1188 q^{15} - 3100 q^{17} + 86 q^{19} + 3272 q^{21} + 3294 q^{23} - 53297 q^{25} + 3894 q^{27} - 3458 q^{29} + 29730 q^{31} + 15944 q^{33} + 2536 q^{35} + 4274 q^{37} - 14324 q^{39} + 9778 q^{41} + 3594 q^{43} - 110377 q^{45} + 43114 q^{47} - 228773 q^{49} + 61449 q^{51} + 48893 q^{53} - 38366 q^{55} + 28823 q^{57} - 36870 q^{59} + 47300 q^{61} + 317893 q^{63} + 39810 q^{65} + 106690 q^{67} - 33916 q^{69} - 114989 q^{71} - 120710 q^{73} + 296522 q^{75} - 28128 q^{77} + 96410 q^{79} - 588917 q^{81} - 250256 q^{83} - 445703 q^{85} - 152816 q^{87} - 567660 q^{89} + 3906 q^{91} - 186593 q^{93} + 97258 q^{95} - 519616 q^{97} + 328234 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(676, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(676, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(676, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)