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Properties

Label 3648.2.bz
Level $3648$
Weight $2$
Character orbit 3648.bz
Rep. character $\chi_{3648}(977,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $624$
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.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 2624 656 1968
Cusp forms 2496 624 1872
Eisenstein series 128 32 96

Trace form

\( 624 q + 6 q^{3} + O(q^{10}) \) \( 624 q + 6 q^{3} - 12 q^{13} + 12 q^{15} + 12 q^{21} - 12 q^{33} + 4 q^{43} + 12 q^{45} - 560 q^{49} + 6 q^{51} + 28 q^{61} - 24 q^{63} + 12 q^{67} + 24 q^{79} - 4 q^{81} - 60 q^{85} - 72 q^{91} + 4 q^{93} - 24 q^{97} + 52 q^{99} + O(q^{100}) \)

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

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