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Properties

Label 1296.2.v
Level $1296$
Weight $2$
Character orbit 1296.v
Rep. character $\chi_{1296}(107,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $376$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1296.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1296, [\chi])\).

Total New Old
Modular forms 912 392 520
Cusp forms 816 376 440
Eisenstein series 96 16 80

Trace form

\( 376 q + 4 q^{4} + 8 q^{7} + O(q^{10}) \) \( 376 q + 4 q^{4} + 8 q^{7} - 8 q^{10} + 4 q^{13} + 4 q^{16} - 8 q^{19} + 4 q^{22} - 40 q^{28} - 4 q^{34} - 8 q^{37} + 4 q^{40} + 4 q^{43} + 128 q^{46} - 156 q^{49} + 4 q^{52} - 16 q^{55} - 32 q^{58} + 4 q^{61} + 64 q^{64} + 4 q^{67} + 32 q^{70} + 64 q^{76} + 48 q^{82} - 16 q^{85} - 116 q^{88} - 64 q^{91} + 12 q^{94} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)