Properties

Label 912.6.bn
Level $912$
Weight $6$
Character orbit 912.bn
Rep. character $\chi_{912}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $396$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(912, [\chi])\).

Total New Old
Modular forms 1624 404 1220
Cusp forms 1576 396 1180
Eisenstein series 48 8 40

Trace form

\( 396 q + 3 q^{3} + 132 q^{7} - 23 q^{9} + O(q^{10}) \) \( 396 q + 3 q^{3} + 132 q^{7} - 23 q^{9} - 6 q^{13} + 3 q^{15} + 2060 q^{19} - 732 q^{21} + 118748 q^{25} - 6408 q^{33} + 490 q^{39} + 32356 q^{43} - 6254 q^{45} + 907796 q^{49} + 3 q^{51} + 1444 q^{55} - 29489 q^{57} + 48078 q^{61} + 38426 q^{63} - 265452 q^{67} - 27346 q^{73} + 113616 q^{79} + 129125 q^{81} - 128470 q^{85} + 140610 q^{87} + 265866 q^{91} + 242 q^{93} + 348870 q^{97} + 25832 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)