Properties

Label 3549.2.di
Level $3549$
Weight $2$
Character orbit 3549.di
Rep. character $\chi_{3549}(131,\cdot)$
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.di (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

\( 11568q - 33q^{3} - 502q^{4} - 50q^{7} - 15q^{9} + O(q^{10}) \) \( 11568q - 33q^{3} - 502q^{4} - 50q^{7} - 15q^{9} - 66q^{10} - 21q^{12} + 40q^{15} + 446q^{16} - 3q^{18} - 138q^{19} - 24q^{21} - 200q^{22} - 75q^{24} + 448q^{25} - 48q^{28} - 37q^{30} - 120q^{31} - 39q^{33} - 84q^{36} - 24q^{37} - 68q^{39} - 42q^{40} - 52q^{42} - 52q^{43} - 33q^{45} - 82q^{46} - 54q^{49} - 3q^{51} - 72q^{52} - 219q^{54} - 158q^{57} + 38q^{58} - 29q^{60} - 30q^{61} - 35q^{63} + 808q^{64} - 48q^{66} + 120q^{67} - 308q^{70} - 75q^{72} - 72q^{73} - 228q^{75} - 32q^{78} + 16q^{79} - 15q^{81} - 150q^{82} + 251q^{84} - 168q^{85} - 99q^{87} - 174q^{88} - 69q^{91} + 55q^{93} + 84q^{94} - 105q^{96} - 36q^{99} + O(q^{100}) \)

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

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