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Properties

Label 3549.2.dc
Level $3549$
Weight $2$
Character orbit 3549.dc
Rep. character $\chi_{3549}(230,\cdot)$
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.dc (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

\( 11568 q - 580 q^{4} - 47 q^{7} - 48 q^{9} + O(q^{10}) \) \( 11568 q - 580 q^{4} - 47 q^{7} - 48 q^{9} - 86 q^{15} + 368 q^{16} - 60 q^{18} - 20 q^{22} - 1028 q^{25} - 90 q^{28} - 76 q^{30} - 78 q^{36} - 96 q^{37} - 128 q^{39} - 10 q^{42} - 118 q^{43} - 172 q^{46} - 45 q^{49} - 48 q^{51} - 86 q^{57} - 52 q^{58} + 64 q^{60} - 98 q^{63} + 808 q^{64} - 210 q^{67} - 248 q^{70} - 114 q^{72} - 50 q^{78} - 92 q^{79} - 60 q^{81} + 239 q^{84} - 132 q^{85} + 24 q^{88} - 45 q^{91} - 68 q^{93} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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