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Properties

Label 3004.2.v
Level $3004$
Weight $2$
Character orbit 3004.v
Rep. character $\chi_{3004}(45,\cdot)$
Character field $\Q(\zeta_{125})$
Dimension $6200$
Sturm bound $752$

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Defining parameters

Level: \( N \) \(=\) \( 3004 = 2^{2} \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3004.v (of order \(125\) and degree \(100\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{125})\)
Sturm bound: \(752\)

Dimensions

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

Total New Old
Modular forms 37900 6200 31700
Cusp forms 37300 6200 31100
Eisenstein series 600 0 600

Trace form

\( 6200 q + O(q^{10}) \) \( 6200 q + 25 q^{13} + 50 q^{15} - 100 q^{39} - 100 q^{51} + 400 q^{53} + 50 q^{57} - 200 q^{63} + 100 q^{67} - 25 q^{71} + 400 q^{73} - 200 q^{77} + 100 q^{79} + 175 q^{83} + 75 q^{85} - 100 q^{89} - 100 q^{93} + 50 q^{97} + 350 q^{99} + O(q^{100}) \)

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

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