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Properties

Label 3450.2.o
Level $3450$
Weight $2$
Character orbit 3450.o
Rep. character $\chi_{3450}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
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.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2912 432 2480
Cusp forms 2848 432 2416
Eisenstein series 64 0 64

Trace form

\( 432 q + 108 q^{4} + 4 q^{6} + 108 q^{9} + O(q^{10}) \) \( 432 q + 108 q^{4} + 4 q^{6} + 108 q^{9} - 4 q^{10} - 4 q^{15} - 108 q^{16} + 16 q^{24} + 4 q^{25} - 16 q^{26} + 20 q^{28} + 16 q^{29} - 12 q^{31} - 24 q^{34} - 24 q^{35} - 108 q^{36} + 4 q^{40} - 88 q^{41} - 20 q^{42} + 8 q^{46} + 40 q^{47} - 376 q^{49} + 8 q^{50} + 80 q^{53} - 4 q^{54} - 104 q^{55} - 48 q^{59} - 16 q^{60} - 64 q^{61} + 108 q^{64} - 16 q^{65} + 80 q^{67} - 8 q^{69} - 12 q^{70} + 40 q^{71} - 40 q^{73} - 16 q^{74} - 16 q^{75} - 160 q^{77} - 8 q^{79} - 108 q^{81} - 120 q^{83} - 20 q^{88} - 72 q^{89} + 4 q^{90} + 48 q^{91} - 48 q^{94} + 40 q^{95} + 4 q^{96} + 20 q^{97} - 160 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)