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Properties

Label 3004.2.m
Level $3004$
Weight $2$
Character orbit 3004.m
Rep. character $\chi_{3004}(437,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $504$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 3032 504 2528
Cusp forms 2984 504 2480
Eisenstein series 48 0 48

Trace form

\( 504 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 69 q^{9} + O(q^{10}) \) \( 504 q + 4 q^{3} - 2 q^{5} + 4 q^{7} + 69 q^{9} - 6 q^{11} + 15 q^{13} - 12 q^{15} + 5 q^{17} + 6 q^{19} - 12 q^{21} - 9 q^{23} + 49 q^{25} + 10 q^{27} - q^{29} - 35 q^{31} - 12 q^{33} + 2 q^{35} + 28 q^{37} + 57 q^{39} + 104 q^{41} - 6 q^{43} + 22 q^{45} - 20 q^{47} - 102 q^{49} - 16 q^{51} - 32 q^{53} - 32 q^{55} + 55 q^{57} + q^{59} + 8 q^{61} + 49 q^{63} + 38 q^{65} + 36 q^{67} - 52 q^{69} - 39 q^{71} - 23 q^{73} - 20 q^{75} - 28 q^{77} - 89 q^{79} + 82 q^{81} + 76 q^{83} + 12 q^{85} - 97 q^{87} - 9 q^{89} + 58 q^{91} - 24 q^{93} + 7 q^{95} - q^{97} - 20 q^{99} + O(q^{100}) \)

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

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