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Properties

Label 3483.2.d
Level $3483$
Weight $2$
Character orbit 3483.d
Rep. character $\chi_{3483}(3482,\cdot)$
Character field $\Q$
Dimension $172$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 3483 = 3^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3483.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 129 \)
Character field: \(\Q\)
Sturm bound: \(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3483, [\chi])\).

Total New Old
Modular forms 408 180 228
Cusp forms 384 172 212
Eisenstein series 24 8 16

Trace form

\( 172 q + 172 q^{4} + O(q^{10}) \) \( 172 q + 172 q^{4} + 196 q^{16} + 160 q^{25} - 12 q^{31} + 24 q^{40} - 92 q^{49} - 36 q^{52} - 36 q^{58} + 208 q^{64} - 36 q^{67} + 48 q^{79} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3483, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3483, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(387, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1161, [\chi])\)\(^{\oplus 2}\)