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Properties

Label 260.4.bg
Level $260$
Weight $4$
Character orbit 260.bg
Rep. character $\chi_{260}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $488$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 260.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(260, [\chi])\).

Total New Old
Modular forms 520 520 0
Cusp forms 488 488 0
Eisenstein series 32 32 0

Trace form

\( 488 q - 6 q^{2} - 12 q^{6} + O(q^{10}) \) \( 488 q - 6 q^{2} - 12 q^{6} - 74 q^{10} + 148 q^{12} + 38 q^{13} - 60 q^{16} + 126 q^{17} - 390 q^{20} - 56 q^{22} - 236 q^{25} + 80 q^{26} - 6 q^{28} - 160 q^{30} - 516 q^{32} - 12 q^{33} - 724 q^{36} - 1002 q^{37} - 40 q^{38} + 548 q^{40} - 24 q^{41} + 164 q^{42} - 1242 q^{45} - 12 q^{46} + 1112 q^{48} - 522 q^{50} + 702 q^{52} + 556 q^{53} - 1812 q^{56} - 4110 q^{58} - 8 q^{61} - 1924 q^{62} - 3092 q^{65} + 8304 q^{66} - 596 q^{68} - 3078 q^{72} - 12 q^{76} + 2728 q^{77} + 6392 q^{78} + 744 q^{80} + 14572 q^{81} - 5170 q^{82} - 12 q^{85} - 4602 q^{88} - 2060 q^{90} + 9732 q^{92} - 336 q^{93} - 12 q^{97} - 126 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(260, [\chi])\) into newform subspaces

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