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Properties

Label 2220.2.db
Level $2220$
Weight $2$
Character orbit 2220.db
Rep. character $\chi_{2220}(29,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 2220 = 2^{2} \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2220.db (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 555 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2220, [\chi])\).

Total New Old
Modular forms 1872 304 1568
Cusp forms 1776 304 1472
Eisenstein series 96 0 96

Trace form

\( 304 q + 4 q^{9} + O(q^{10}) \) \( 304 q + 4 q^{9} - 8 q^{15} + 8 q^{19} - 24 q^{31} - 8 q^{39} - 26 q^{45} + 144 q^{49} - 16 q^{51} + 20 q^{55} + 72 q^{61} + 28 q^{69} + 80 q^{75} - 36 q^{81} + 64 q^{91} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2220, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2220, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2220, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)