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Properties

Label 1608.2.j
Level $1608$
Weight $2$
Character orbit 1608.j
Rep. character $\chi_{1608}(1475,\cdot)$
Character field $\Q$
Dimension $264$
Sturm bound $544$

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Defining parameters

Level: \( N \) \(=\) \( 1608 = 2^{3} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1608.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(544\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1608, [\chi])\).

Total New Old
Modular forms 276 264 12
Cusp forms 268 264 4
Eisenstein series 8 0 8

Trace form

\( 264 q + 4 q^{4} - 6 q^{6} + O(q^{10}) \) \( 264 q + 4 q^{4} - 6 q^{6} - 12 q^{10} - 16 q^{12} - 4 q^{16} + 18 q^{18} - 16 q^{19} - 8 q^{22} + 4 q^{24} + 264 q^{25} - 24 q^{27} + 14 q^{30} - 24 q^{34} - 14 q^{36} - 40 q^{40} + 32 q^{42} + 32 q^{43} + 4 q^{46} - 18 q^{48} - 264 q^{49} + 40 q^{51} + 24 q^{52} + 4 q^{54} - 20 q^{58} - 14 q^{60} + 40 q^{64} - 22 q^{66} + 4 q^{70} + 32 q^{72} - 56 q^{75} - 52 q^{76} + 24 q^{78} + 20 q^{82} + 70 q^{84} - 44 q^{88} + 42 q^{90} - 28 q^{96} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1608, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1608, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)