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Properties

Label 3042.2.bl
Level $3042$
Weight $2$
Character orbit 3042.bl
Rep. character $\chi_{3042}(79,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $4368$
Sturm bound $1092$

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Defining parameters

Level: \( N \) \(=\) \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3042.bl (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3042, [\chi])\).

Total New Old
Modular forms 13200 4368 8832
Cusp forms 13008 4368 8640
Eisenstein series 192 0 192

Trace form

\( 4368 q + 182 q^{4} + 4 q^{7} - 16 q^{9} + O(q^{10}) \) \( 4368 q + 182 q^{4} + 4 q^{7} - 16 q^{9} - 8 q^{11} - 24 q^{13} + 8 q^{14} + 96 q^{15} + 182 q^{16} - 16 q^{17} + 16 q^{18} - 8 q^{19} - 8 q^{21} - 8 q^{23} + 182 q^{25} + 8 q^{26} - 24 q^{27} - 8 q^{28} + 16 q^{29} - 110 q^{30} + 4 q^{31} + 52 q^{33} + 24 q^{35} + 8 q^{36} - 8 q^{37} - 52 q^{39} - 16 q^{41} + 20 q^{42} + 4 q^{43} + 16 q^{44} + 232 q^{45} - 34 q^{47} + 186 q^{49} - 8 q^{50} - 126 q^{51} + 2 q^{52} - 88 q^{53} + 120 q^{54} + 8 q^{56} - 62 q^{57} + 32 q^{59} + 16 q^{60} + 28 q^{61} - 8 q^{62} - 166 q^{63} - 364 q^{64} - 8 q^{65} - 48 q^{66} + 28 q^{67} + 8 q^{68} + 4 q^{69} + 48 q^{71} - 8 q^{72} - 56 q^{73} + 8 q^{74} + 106 q^{75} + 4 q^{76} + 8 q^{77} + 6 q^{78} - 20 q^{79} + 8 q^{81} - 48 q^{82} + 154 q^{83} - 8 q^{84} - 16 q^{86} + 68 q^{87} - 416 q^{89} - 40 q^{90} - 8 q^{91} - 8 q^{92} + 284 q^{93} + 28 q^{97} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3042, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3042, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3042, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1521, [\chi])\)\(^{\oplus 2}\)