Properties

Label 3450.2.i
Level $3450$
Weight $2$
Character orbit 3450.i
Rep. character $\chi_{3450}(2393,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $264$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 264 1224
Cusp forms 1392 264 1128
Eisenstein series 96 0 96

Trace form

\( 264 q - 8 q^{7} + O(q^{10}) \) \( 264 q - 8 q^{7} - 16 q^{13} - 264 q^{16} + 32 q^{21} + 8 q^{22} - 8 q^{28} + 16 q^{31} - 16 q^{33} - 32 q^{36} - 16 q^{37} + 8 q^{42} + 24 q^{51} + 16 q^{52} - 48 q^{57} - 40 q^{58} - 16 q^{61} + 64 q^{63} - 24 q^{66} + 32 q^{67} + 8 q^{73} - 16 q^{76} - 24 q^{78} - 32 q^{81} - 64 q^{82} + 32 q^{87} + 8 q^{88} - 192 q^{91} - 88 q^{93} + 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)