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Properties

Label 3450.2.bt
Level $3450$
Weight $2$
Character orbit 3450.bt
Rep. character $\chi_{3450}(37,\cdot)$
Character field $\Q(\zeta_{220})$
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.bt (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 58240 9600 48640
Cusp forms 56960 9600 47360
Eisenstein series 1280 0 1280

Trace form

\( 9600 q + O(q^{10}) \) \( 9600 q + 16 q^{13} - 240 q^{16} + 632 q^{23} - 32 q^{25} - 88 q^{28} + 160 q^{29} + 64 q^{35} + 240 q^{36} - 88 q^{37} + 656 q^{47} + 16 q^{50} + 16 q^{52} + 48 q^{55} - 88 q^{57} - 160 q^{59} - 64 q^{62} - 160 q^{70} + 96 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 240 q^{81} - 112 q^{82} - 136 q^{85} + 112 q^{87} + 8 q^{92} - 32 q^{93} + 680 q^{95} + 144 q^{98} + O(q^{100}) \)

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

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