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Properties

Label 676.6.h
Level $676$
Weight $6$
Character orbit 676.h
Rep. character $\chi_{676}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $130$
Sturm bound $546$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 952 130 822
Cusp forms 868 130 738
Eisenstein series 84 0 84

Trace form

\( 130 q - 9 q^{3} + 87 q^{7} - 5618 q^{9} + O(q^{10}) \) \( 130 q - 9 q^{3} + 87 q^{7} - 5618 q^{9} + 297 q^{11} + 1056 q^{15} + 1369 q^{17} + 111 q^{19} - 879 q^{23} - 84286 q^{25} - 8166 q^{27} - 2633 q^{29} + 4875 q^{33} - 16940 q^{35} - 3627 q^{37} - 3 q^{41} - 2153 q^{43} - 24750 q^{45} + 158170 q^{49} - 38182 q^{51} - 56544 q^{53} - 14060 q^{55} + 71175 q^{59} + 337 q^{61} + 128502 q^{63} + 10821 q^{67} + 25791 q^{69} - 77973 q^{71} + 94245 q^{75} - 157014 q^{77} - 241460 q^{79} - 650705 q^{81} + 169002 q^{85} - 43567 q^{87} + 426687 q^{89} + 31470 q^{93} - 5714 q^{95} - 273609 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(676, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)