Properties

Label 3549.2.dp
Level $3549$
Weight $2$
Character orbit 3549.dp
Rep. character $\chi_{3549}(38,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $11568$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.dp (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3549 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 11760 11760 0
Cusp forms 11568 11568 0
Eisenstein series 192 192 0

Trace form

\( 11568q - 33q^{3} + 458q^{4} - 52q^{7} - 7q^{9} + O(q^{10}) \) \( 11568q - 33q^{3} + 458q^{4} - 52q^{7} - 7q^{9} - 66q^{10} - 45q^{12} - 156q^{15} + 462q^{16} - 13q^{18} - 26q^{21} - 184q^{22} - 39q^{24} - 492q^{25} - 52q^{28} - 49q^{30} - 78q^{31} - 39q^{33} - 100q^{36} - 26q^{37} - 74q^{39} + 30q^{40} - 28q^{42} - 84q^{43} - 39q^{45} - 130q^{46} - 54q^{49} - 35q^{51} - 108q^{52} + 195q^{54} + 26q^{57} - 78q^{58} - 13q^{60} - 102q^{61} - 91q^{63} - 1000q^{64} - 216q^{66} + 26q^{67} - 13q^{72} - 78q^{73} - 168q^{75} + 16q^{78} - 12q^{79} - 47q^{81} - 198q^{82} - 273q^{84} - 104q^{85} - 99q^{87} - 142q^{88} - 13q^{91} - 13q^{93} - 12q^{94} - 39q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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