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Properties

Label 1900.3.cc
Level $1900$
Weight $3$
Character orbit 1900.cc
Rep. character $\chi_{1900}(143,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $4272$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.cc (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 7344 4368 2976
Cusp forms 7056 4272 2784
Eisenstein series 288 96 192

Trace form

\( 4272 q + 12 q^{2} - 96 q^{6} + 18 q^{8} + O(q^{10}) \) \( 4272 q + 12 q^{2} - 96 q^{6} + 18 q^{8} + 18 q^{12} + 24 q^{13} - 192 q^{16} + 24 q^{17} - 48 q^{21} + 36 q^{22} + 276 q^{26} - 408 q^{28} - 198 q^{32} + 132 q^{33} + 264 q^{36} + 294 q^{38} - 144 q^{41} + 228 q^{42} - 36 q^{46} + 936 q^{48} + 12 q^{52} + 24 q^{53} + 24 q^{57} + 168 q^{58} - 48 q^{61} + 768 q^{62} - 456 q^{66} + 6 q^{68} + 168 q^{72} + 24 q^{73} + 984 q^{76} + 1512 q^{77} - 534 q^{78} - 48 q^{81} - 1068 q^{82} + 624 q^{86} + 18 q^{88} - 588 q^{92} - 84 q^{93} - 3312 q^{96} + 24 q^{97} - 258 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)