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Properties

Label 912.6.cq
Level $912$
Weight $6$
Character orbit 912.cq
Rep. character $\chi_{912}(61,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $4800$
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.cq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 9648 4800 4848
Cusp forms 9552 4800 4752
Eisenstein series 96 0 96

Trace form

\( 4800 q + O(q^{10}) \) \( 4800 q - 2904 q^{10} + 3660 q^{16} - 138384 q^{31} - 76740 q^{32} + 38280 q^{34} + 4860 q^{36} - 119148 q^{38} + 93540 q^{40} + 150060 q^{46} + 5762400 q^{49} + 205596 q^{50} - 31320 q^{51} + 27408 q^{52} + 43740 q^{54} - 10728 q^{68} - 66960 q^{69} + 215208 q^{70} - 344208 q^{76} - 454248 q^{78} - 739320 q^{80} - 550920 q^{82} + 794400 q^{85} + 670152 q^{94} + 967764 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{6}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)