Properties

Label 1980.2.ce
Level $1980$
Weight $2$
Character orbit 1980.ce
Rep. character $\chi_{1980}(353,\cdot)$
Character field $\Q(\zeta_{12})$
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.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1776 240 1536
Cusp forms 1680 240 1440
Eisenstein series 96 0 96

Trace form

\( 240 q + 2 q^{3} + O(q^{10}) \) \( 240 q + 2 q^{3} - 16 q^{15} + 48 q^{23} - 6 q^{25} + 44 q^{27} + 4 q^{33} - 12 q^{37} + 72 q^{41} + 52 q^{45} + 72 q^{47} + 32 q^{51} - 12 q^{55} + 60 q^{57} + 24 q^{61} - 48 q^{63} + 48 q^{65} - 6 q^{67} - 24 q^{75} - 12 q^{81} + 48 q^{85} - 112 q^{87} - 118 q^{93} - 120 q^{95} + 42 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)