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Properties

Label 912.3.bl
Level $912$
Weight $3$
Character orbit 912.bl
Rep. character $\chi_{912}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $156$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 664 164 500
Cusp forms 616 156 460
Eisenstein series 48 8 40

Trace form

\( 156 q + q^{3} - 8 q^{7} - 5 q^{9} + O(q^{10}) \) \( 156 q + q^{3} - 8 q^{7} - 5 q^{9} - 2 q^{13} + 19 q^{15} - 12 q^{19} - 10 q^{21} + 348 q^{25} + 4 q^{27} - 168 q^{31} + 20 q^{33} - 8 q^{37} - 14 q^{39} - 110 q^{43} - 54 q^{45} + 932 q^{49} + 19 q^{51} + 71 q^{57} + 30 q^{61} - 22 q^{63} - 62 q^{67} - 22 q^{69} + 62 q^{73} - 28 q^{75} + 186 q^{79} - 133 q^{81} - 6 q^{85} + 246 q^{87} + 548 q^{91} - 10 q^{93} - 10 q^{97} - 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

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