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Properties

Label 3450.2.bn
Level $3450$
Weight $2$
Character orbit 3450.bn
Rep. character $\chi_{3450}(89,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $9600$
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.bn (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1725 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 29120 9600 19520
Cusp forms 28480 9600 18880
Eisenstein series 640 0 640

Trace form

\( 9600 q + 240 q^{4} + 8 q^{9} + O(q^{10}) \) \( 9600 q + 240 q^{4} + 8 q^{9} + 20 q^{12} - 22 q^{15} + 240 q^{16} - 56 q^{25} - 44 q^{30} - 48 q^{31} + 8 q^{36} - 24 q^{39} + 12 q^{46} - 20 q^{48} - 1024 q^{49} + 52 q^{55} + 22 q^{60} + 240 q^{64} - 346 q^{69} + 152 q^{70} - 120 q^{73} - 526 q^{75} + 100 q^{78} + 116 q^{81} + 116 q^{85} - 100 q^{87} + 16 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)