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Properties

Label 3450.2.bs
Level $3450$
Weight $2$
Character orbit 3450.bs
Rep. character $\chi_{3450}(77,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $19200$
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.bs (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1725 \)
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 19200 39040
Cusp forms 56960 19200 37760
Eisenstein series 1280 0 1280

Trace form

\( 19200 q - 8 q^{3} + O(q^{10}) \) \( 19200 q - 8 q^{3} + 8 q^{12} + 16 q^{13} - 8 q^{15} - 480 q^{16} - 72 q^{18} + 80 q^{19} + 64 q^{22} + 208 q^{25} - 8 q^{27} - 36 q^{33} - 24 q^{37} + 80 q^{39} + 48 q^{43} + 8 q^{48} - 16 q^{52} + 64 q^{55} + 16 q^{57} - 48 q^{60} + 8 q^{63} - 64 q^{67} - 140 q^{69} - 144 q^{70} - 16 q^{72} - 208 q^{73} - 164 q^{75} - 176 q^{78} - 160 q^{79} + 80 q^{81} - 128 q^{82} - 64 q^{85} + 8 q^{87} - 16 q^{88} - 40 q^{90} + 64 q^{93} + 264 q^{97} + O(q^{100}) \)

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

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