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Properties

Label 3648.2.cm
Level $3648$
Weight $2$
Character orbit 3648.cm
Rep. character $\chi_{3648}(341,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $5088$
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.cm (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3648 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 5152 5152 0
Cusp forms 5088 5088 0
Eisenstein series 64 64 0

Trace form

\( 5088 q - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} + O(q^{10}) \) \( 5088 q - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{16} - 16 q^{19} - 16 q^{24} - 32 q^{25} - 32 q^{28} - 16 q^{30} - 16 q^{36} - 16 q^{39} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{49} - 16 q^{54} - 32 q^{55} - 8 q^{57} - 32 q^{58} - 32 q^{61} - 32 q^{63} + 160 q^{64} + 16 q^{66} - 32 q^{73} - 128 q^{76} - 16 q^{81} - 32 q^{82} - 32 q^{85} - 16 q^{87} - 64 q^{93} - 288 q^{96} - 16 q^{99} + O(q^{100}) \)

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.