Properties

Label 3600.2.cu
Level $3600$
Weight $2$
Character orbit 3600.cu
Rep. character $\chi_{3600}(349,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.cu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 720 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

Total New Old
Modular forms 2928 1744 1184
Cusp forms 2832 1712 1120
Eisenstein series 96 32 64

Trace form

\( 1712 q + 4 q^{4} - 8 q^{6} + O(q^{10}) \) \( 1712 q + 4 q^{4} - 8 q^{6} - 4 q^{11} + 20 q^{14} - 4 q^{16} + 16 q^{19} - 20 q^{21} - 24 q^{24} + 48 q^{26} + 4 q^{29} - 8 q^{31} + 12 q^{34} + 16 q^{36} + 16 q^{44} - 80 q^{46} - 800 q^{49} - 32 q^{51} + 120 q^{54} + 24 q^{56} + 4 q^{59} - 4 q^{61} + 16 q^{64} + 184 q^{66} + 20 q^{69} + 4 q^{74} - 28 q^{76} + 8 q^{79} - 16 q^{81} + 244 q^{84} + 36 q^{86} - 72 q^{91} - 12 q^{94} - 184 q^{96} + 108 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)