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Properties

Label 2128.2.dx
Level $2128$
Weight $2$
Character orbit 2128.dx
Rep. character $\chi_{2128}(115,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 2128 = 2^{4} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2128.dx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2128, [\chi])\).

Total New Old
Modular forms 1296 1152 144
Cusp forms 1264 1152 112
Eisenstein series 32 0 32

Trace form

\( 1152 q + 4 q^{4} + O(q^{10}) \) \( 1152 q + 4 q^{4} - 8 q^{11} - 32 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 24 q^{28} + 32 q^{29} + 40 q^{30} + 20 q^{32} - 80 q^{36} - 16 q^{37} + 120 q^{40} - 60 q^{42} - 16 q^{43} - 12 q^{44} - 56 q^{50} + 40 q^{51} - 180 q^{52} - 16 q^{53} - 168 q^{54} - 12 q^{58} - 96 q^{59} - 96 q^{60} - 56 q^{64} - 40 q^{67} + 4 q^{70} + 128 q^{71} - 20 q^{72} - 72 q^{74} - 104 q^{78} + 576 q^{81} - 120 q^{82} + 180 q^{84} - 4 q^{86} - 64 q^{88} + 16 q^{91} + 56 q^{92} + 72 q^{94} + 120 q^{96} + 80 q^{98} - 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2128, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2128, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2128, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)