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Properties

Label 1980.2.bu
Level $1980$
Weight $2$
Character orbit 1980.bu
Rep. character $\chi_{1980}(271,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1980.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1980, [\chi])\).

Total New Old
Modular forms 1792 480 1312
Cusp forms 1664 480 1184
Eisenstein series 128 0 128

Trace form

\( 480 q - 4 q^{4} + O(q^{10}) \) \( 480 q - 4 q^{4} - 10 q^{14} - 8 q^{16} + 4 q^{20} + 52 q^{22} - 120 q^{25} - 20 q^{26} - 10 q^{28} + 20 q^{34} - 48 q^{37} + 10 q^{38} - 20 q^{41} - 14 q^{44} + 10 q^{46} - 132 q^{49} + 50 q^{52} - 64 q^{53} + 72 q^{56} + 58 q^{58} + 8 q^{64} + 130 q^{68} + 40 q^{70} + 120 q^{74} + 24 q^{80} - 108 q^{82} - 4 q^{86} + 56 q^{88} + 48 q^{89} + 72 q^{92} - 120 q^{94} + 44 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1980, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)