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Properties

Label 3648.2.dx
Level $3648$
Weight $2$
Character orbit 3648.dx
Rep. character $\chi_{3648}(11,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $10176$
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.dx (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3648 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1280\)

Dimensions

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

Total New Old
Modular forms 10304 10304 0
Cusp forms 10176 10176 0
Eisenstein series 128 128 0

Trace form

\( 10176 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 64 q^{7} - 8 q^{9} + O(q^{10}) \) \( 10176 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 64 q^{7} - 8 q^{9} - 16 q^{10} - 32 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 32 q^{18} - 32 q^{19} - 8 q^{21} - 16 q^{22} - 8 q^{24} - 16 q^{25} - 32 q^{27} - 16 q^{28} - 32 q^{30} - 128 q^{31} - 16 q^{34} - 8 q^{36} - 64 q^{37} - 32 q^{39} - 16 q^{40} - 8 q^{42} - 16 q^{43} - 32 q^{45} - 64 q^{46} - 8 q^{48} - 64 q^{49} - 8 q^{51} - 16 q^{52} - 8 q^{54} - 16 q^{55} - 16 q^{57} - 64 q^{58} - 8 q^{60} - 16 q^{61} - 256 q^{64} + 24 q^{66} - 16 q^{67} - 32 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 32 q^{75} - 144 q^{76} - 8 q^{78} + 48 q^{79} - 8 q^{81} - 16 q^{82} - 32 q^{84} - 16 q^{85} - 32 q^{87} - 224 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} - 256 q^{94} + 512 q^{96} - 8 q^{99} + O(q^{100}) \)

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.