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Properties

Label 1980.2.cn
Level $1980$
Weight $2$
Character orbit 1980.cn
Rep. character $\chi_{1980}(73,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
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.cn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3648 240 3408
Cusp forms 3264 240 3024
Eisenstein series 384 0 384

Trace form

\( 240 q + 4 q^{5} + 10 q^{7} + O(q^{10}) \) \( 240 q + 4 q^{5} + 10 q^{7} + 8 q^{11} + 10 q^{17} + 22 q^{25} - 16 q^{31} - 2 q^{37} - 20 q^{41} + 6 q^{47} - 42 q^{53} + 22 q^{55} + 40 q^{61} + 56 q^{67} - 4 q^{71} + 20 q^{73} + 60 q^{77} + 40 q^{85} + 56 q^{91} + 50 q^{95} + 54 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)