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Properties

Label 1312.2.cz
Level $1312$
Weight $2$
Character orbit 1312.cz
Rep. character $\chi_{1312}(15,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $640$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1312 = 2^{5} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1312.cz (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 328 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1312, [\chi])\).

Total New Old
Modular forms 2816 704 2112
Cusp forms 2560 640 1920
Eisenstein series 256 64 192

Trace form

\( 640 q + 32 q^{3} - 32 q^{9} + O(q^{10}) \) \( 640 q + 32 q^{3} - 32 q^{9} + 32 q^{11} - 40 q^{17} + 32 q^{19} - 40 q^{25} + 32 q^{27} - 48 q^{33} - 16 q^{35} - 24 q^{41} + 32 q^{43} - 32 q^{49} + 24 q^{51} - 24 q^{57} - 72 q^{59} - 32 q^{65} - 16 q^{67} - 32 q^{73} + 120 q^{75} + 64 q^{83} - 32 q^{89} + 128 q^{91} - 24 q^{97} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1312, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 2}\)