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Properties

Label 3483.2.bo
Level $3483$
Weight $2$
Character orbit 3483.bo
Rep. character $\chi_{3483}(130,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $6804$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 3483 = 3^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3483.bo (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 7164 6804 360
Cusp forms 7092 6804 288
Eisenstein series 72 0 72

Trace form

\( 6804 q + O(q^{10}) \) \( 6804 q - 72 q^{20} - 54 q^{21} - 54 q^{23} - 108 q^{24} - 54 q^{27} - 54 q^{29} - 108 q^{32} - 54 q^{33} - 54 q^{35} - 72 q^{36} - 90 q^{42} - 144 q^{44} - 108 q^{47} - 198 q^{48} - 108 q^{53} - 126 q^{54} - 126 q^{56} - 108 q^{57} - 198 q^{62} - 108 q^{63} + 72 q^{65} - 54 q^{67} - 90 q^{68} + 144 q^{71} + 432 q^{72} + 180 q^{75} + 288 q^{77} - 108 q^{79} - 108 q^{85} + 288 q^{87} + 180 q^{89} + 252 q^{92} - 36 q^{93} - 216 q^{95} - 54 q^{97} - 198 q^{98} - 144 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3483, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)