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Properties

Label 3456.2.bw
Level $3456$
Weight $2$
Character orbit 3456.bw
Rep. character $\chi_{3456}(97,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1680$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.bw (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3456, [\chi])\).

Total New Old
Modular forms 7104 1776 5328
Cusp forms 6720 1680 5040
Eisenstein series 384 96 288

Trace form

\( 1680 q + 24 q^{5} + O(q^{10}) \) \( 1680 q + 24 q^{5} + 24 q^{13} - 24 q^{17} + 24 q^{21} + 24 q^{29} - 48 q^{33} + 12 q^{37} + 24 q^{45} - 48 q^{49} + 48 q^{53} + 24 q^{61} - 48 q^{65} + 24 q^{69} + 24 q^{77} - 48 q^{81} - 36 q^{85} + 24 q^{93} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)