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Properties

Label 3002.2.m
Level $3002$
Weight $2$
Character orbit 3002.m
Rep. character $\chi_{3002}(103,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $264$
Sturm bound $800$

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Defining parameters

Level: \( N \) \(=\) \( 3002 = 2 \cdot 19 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3002.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1501 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3002, [\chi])\).

Total New Old
Modular forms 808 264 544
Cusp forms 792 264 528
Eisenstein series 16 0 16

Trace form

\( 264 q + 132 q^{4} + 6 q^{7} - 128 q^{9} + O(q^{10}) \) \( 264 q + 132 q^{4} + 6 q^{7} - 128 q^{9} - 30 q^{15} - 132 q^{16} - 6 q^{19} - 12 q^{21} - 8 q^{23} + 264 q^{25} + 36 q^{27} + 12 q^{29} - 30 q^{30} + 18 q^{31} - 18 q^{33} + 24 q^{34} + 30 q^{35} + 128 q^{36} + 6 q^{37} - 18 q^{38} - 42 q^{39} + 6 q^{41} + 40 q^{42} - 6 q^{43} - 8 q^{45} + 18 q^{47} + 122 q^{49} - 12 q^{52} - 18 q^{53} - 18 q^{54} - 2 q^{55} + 36 q^{57} + 42 q^{59} - 60 q^{60} - 2 q^{62} - 264 q^{64} - 60 q^{69} + 24 q^{70} + 104 q^{73} + 24 q^{75} - 12 q^{76} + 42 q^{77} + 30 q^{78} - 6 q^{79} - 108 q^{81} - 12 q^{83} - 12 q^{84} - 18 q^{86} + 52 q^{87} - 72 q^{89} - 18 q^{91} + 8 q^{92} - 54 q^{93} + 24 q^{94} - 72 q^{95} + 12 q^{97} - 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3002, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1501, [\chi])\)\(^{\oplus 2}\)