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Properties

Label 3004.2.e
Level $3004$
Weight $2$
Character orbit 3004.e
Rep. character $\chi_{3004}(1429,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $126$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(752\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3004, [\chi])\).

Total New Old
Modular forms 758 126 632
Cusp forms 746 126 620
Eisenstein series 12 0 12

Trace form

\( 126 q + q^{3} + 2 q^{5} - 4 q^{7} - 64 q^{9} + O(q^{10}) \) \( 126 q + q^{3} + 2 q^{5} - 4 q^{7} - 64 q^{9} - 4 q^{11} + 2 q^{15} - 5 q^{17} - 6 q^{19} - 8 q^{21} - q^{23} - 59 q^{25} + 10 q^{27} + q^{29} + 2 q^{33} - 2 q^{35} - 3 q^{37} + 3 q^{39} + 6 q^{41} + 6 q^{43} - 52 q^{45} + 102 q^{49} + 6 q^{51} - 8 q^{53} + 22 q^{55} - 10 q^{57} - 11 q^{59} - 8 q^{61} + 6 q^{63} + 7 q^{65} + 4 q^{67} - 8 q^{69} - 16 q^{71} + 18 q^{73} + 20 q^{75} + 13 q^{77} - 11 q^{79} - 47 q^{81} + 4 q^{83} - 22 q^{85} - 3 q^{87} + 4 q^{89} - 3 q^{91} + 14 q^{93} - 12 q^{95} + q^{97} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3004, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(751, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1502, [\chi])\)\(^{\oplus 2}\)