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Properties

Label 1980.2.dn
Level $1980$
Weight $2$
Character orbit 1980.dn
Rep. character $\chi_{1980}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1152$
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.dn (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 7104 1152 5952
Cusp forms 6720 1152 5568
Eisenstein series 384 0 384

Trace form

\( 1152 q - 2 q^{3} + O(q^{10}) \) \( 1152 q - 2 q^{3} - 4 q^{11} + 4 q^{15} - 16 q^{23} - 6 q^{25} - 8 q^{27} - 28 q^{33} + 12 q^{37} + 32 q^{45} - 4 q^{47} + 40 q^{51} + 72 q^{53} + 80 q^{57} - 24 q^{67} - 8 q^{71} - 52 q^{75} - 48 q^{77} + 68 q^{81} - 72 q^{91} + 2 q^{93} - 6 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)