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Properties

Label 3648.2.dq
Level $3648$
Weight $2$
Character orbit 3648.dq
Rep. character $\chi_{3648}(401,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1872$
Sturm bound $1280$

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Defining parameters

Level: \( N \) \(=\) \( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3648.dq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

Total New Old
Modular forms 7872 1968 5904
Cusp forms 7488 1872 5616
Eisenstein series 384 96 288

Trace form

\( 1872 q + 12 q^{3} + O(q^{10}) \) \( 1872 q + 12 q^{3} - 24 q^{13} + 24 q^{15} + 24 q^{19} - 30 q^{21} + 18 q^{27} + 72 q^{31} - 24 q^{33} + 24 q^{43} - 6 q^{45} + 768 q^{49} + 12 q^{51} - 24 q^{61} + 108 q^{63} + 24 q^{67} - 18 q^{69} + 48 q^{79} - 24 q^{81} - 120 q^{85} + 108 q^{91} - 30 q^{93} - 48 q^{97} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)