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Properties

Label 3450.2.e
Level $3450$
Weight $2$
Character orbit 3450.e
Rep. character $\chi_{3450}(551,\cdot)$
Character field $\Q$
Dimension $152$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3450.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3450, [\chi])\).

Total New Old
Modular forms 744 152 592
Cusp forms 696 152 544
Eisenstein series 48 0 48

Trace form

\( 152 q + 4 q^{3} - 152 q^{4} + 4 q^{6} + O(q^{10}) \) \( 152 q + 4 q^{3} - 152 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} + 152 q^{16} - 4 q^{24} - 20 q^{27} - 16 q^{31} - 24 q^{39} - 24 q^{46} + 4 q^{48} - 120 q^{49} - 8 q^{52} + 20 q^{54} + 8 q^{58} - 152 q^{64} - 16 q^{69} + 40 q^{73} + 40 q^{78} + 24 q^{81} + 32 q^{82} + 16 q^{87} + 16 q^{93} - 56 q^{94} + 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)