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Properties

Label 912.3.ct
Level $912$
Weight $3$
Character orbit 912.ct
Rep. character $\chi_{912}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1920$
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.ct (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3888 1920 1968
Cusp forms 3792 1920 1872
Eisenstein series 96 0 96

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q + 48 q^{10} - 84 q^{16} + 420 q^{32} - 360 q^{34} - 36 q^{36} - 588 q^{38} + 540 q^{40} - 1620 q^{46} + 6720 q^{49} + 1404 q^{50} + 288 q^{51} + 240 q^{52} - 108 q^{54} + 360 q^{68} - 864 q^{69} - 504 q^{70} + 528 q^{76} - 648 q^{78} - 120 q^{80} + 360 q^{82} - 960 q^{85} - 1092 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)