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Properties

Label 3520.2.fe
Level $3520$
Weight $2$
Character orbit 3520.fe
Rep. character $\chi_{3520}(19,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $18304$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.fe (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3520 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

Total New Old
Modular forms 18560 18560 0
Cusp forms 18304 18304 0
Eisenstein series 256 256 0

Trace form

\( 18304 q - 48 q^{4} - 24 q^{5} - 80 q^{6} - 48 q^{9} + O(q^{10}) \) \( 18304 q - 48 q^{4} - 24 q^{5} - 80 q^{6} - 48 q^{9} - 64 q^{11} - 48 q^{14} - 24 q^{15} - 48 q^{16} - 80 q^{19} - 24 q^{20} - 80 q^{24} - 24 q^{25} + 192 q^{26} - 80 q^{29} - 40 q^{30} - 96 q^{31} - 128 q^{34} - 40 q^{35} - 48 q^{36} - 80 q^{39} - 40 q^{40} - 80 q^{41} - 64 q^{44} - 64 q^{45} - 80 q^{46} - 48 q^{49} - 40 q^{50} - 80 q^{51} + 32 q^{55} - 320 q^{56} + 16 q^{59} - 120 q^{60} - 80 q^{61} - 336 q^{64} - 48 q^{69} - 120 q^{70} - 112 q^{71} - 80 q^{74} + 168 q^{75} - 80 q^{79} - 24 q^{80} - 48 q^{81} - 80 q^{84} - 40 q^{85} - 48 q^{86} - 128 q^{89} - 40 q^{90} - 48 q^{91} - 80 q^{94} - 80 q^{95} - 80 q^{96} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

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