Properties

Label 3520.2.fm
Level $3520$
Weight $2$
Character orbit 3520.fm
Rep. character $\chi_{3520}(13,\cdot)$
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.fm (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

\( 18304 q - 40 q^{2} - 24 q^{3} - 24 q^{5} - 80 q^{6} - 40 q^{7} - 40 q^{8} + O(q^{10}) \) \( 18304 q - 40 q^{2} - 24 q^{3} - 24 q^{5} - 80 q^{6} - 40 q^{7} - 40 q^{8} - 64 q^{11} - 128 q^{12} - 40 q^{13} + 32 q^{14} - 24 q^{15} - 48 q^{16} - 80 q^{17} - 40 q^{18} - 24 q^{20} - 64 q^{23} - 24 q^{25} - 48 q^{26} - 24 q^{27} - 40 q^{28} - 40 q^{30} - 64 q^{34} - 40 q^{35} - 48 q^{36} - 24 q^{37} - 24 q^{38} - 40 q^{40} - 80 q^{41} - 24 q^{42} - 16 q^{45} - 80 q^{46} - 48 q^{47} - 24 q^{48} - 40 q^{50} - 80 q^{51} - 40 q^{52} - 24 q^{53} - 32 q^{55} + 64 q^{56} - 40 q^{57} - 24 q^{58} - 24 q^{60} - 80 q^{61} - 40 q^{62} - 80 q^{63} - 160 q^{66} - 64 q^{67} - 40 q^{68} - 24 q^{70} + 16 q^{71} - 640 q^{72} - 40 q^{73} - 24 q^{75} - 32 q^{77} - 64 q^{78} - 24 q^{80} - 48 q^{81} - 104 q^{82} - 40 q^{83} - 40 q^{85} - 48 q^{86} + 56 q^{88} - 40 q^{90} - 48 q^{91} + 280 q^{92} - 72 q^{93} - 80 q^{96} - 128 q^{99} + O(q^{100}) \)

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

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