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Properties

Label 3004.2.u
Level $3004$
Weight $2$
Character orbit 3004.u
Rep. character $\chi_{3004}(61,\cdot)$
Character field $\Q(\zeta_{75})$
Dimension $2520$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.u (of order \(75\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{75})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 15160 2520 12640
Cusp forms 14920 2520 12400
Eisenstein series 240 0 240

Trace form

\( 2520 q - 5 q^{3} - 5 q^{9} + O(q^{10}) \) \( 2520 q - 5 q^{3} - 5 q^{9} + 10 q^{11} + 60 q^{13} + 60 q^{15} + 20 q^{21} + 10 q^{23} + 10 q^{25} - 20 q^{27} - 140 q^{31} + 10 q^{33} - 25 q^{37} + 140 q^{39} - 110 q^{41} + 30 q^{45} + 20 q^{47} - 90 q^{51} - 60 q^{53} + 10 q^{55} - 20 q^{57} + 10 q^{59} - 255 q^{63} - 45 q^{65} + 60 q^{67} + 60 q^{69} + 30 q^{71} - 95 q^{73} - 185 q^{77} - 100 q^{79} - 35 q^{81} + 95 q^{83} + 85 q^{85} + 100 q^{87} - 95 q^{89} - 55 q^{91} + 210 q^{93} + 5 q^{95} - 100 q^{97} + 430 q^{99} + O(q^{100}) \)

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

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