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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

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

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.