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Properties

Label 1312.2.bu
Level $1312$
Weight $2$
Character orbit 1312.bu
Rep. character $\chi_{1312}(353,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $168$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1312 = 2^{5} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1312.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 704 168 536
Cusp forms 640 168 472
Eisenstein series 64 0 64

Trace form

\( 168 q - 4 q^{5} - 160 q^{9} + O(q^{10}) \) \( 168 q - 4 q^{5} - 160 q^{9} - 16 q^{21} - 54 q^{25} - 40 q^{29} - 12 q^{33} + 30 q^{37} + 14 q^{41} + 4 q^{45} + 58 q^{49} - 32 q^{57} + 20 q^{61} + 30 q^{65} - 12 q^{73} + 72 q^{81} - 120 q^{89} + 80 q^{93} - 30 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 2}\)