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Properties

Label 2006.2.r
Level $2006$
Weight $2$
Character orbit 2006.r
Rep. character $\chi_{2006}(9,\cdot)$
Character field $\Q(\zeta_{232})$
Dimension $10080$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2006.r (of order \(232\) and degree \(112\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{232})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2006, [\chi])\).

Total New Old
Modular forms 30688 10080 20608
Cusp forms 29792 10080 19712
Eisenstein series 896 0 896

Trace form

\( 10080 q + 8 q^{9} + O(q^{10}) \) \( 10080 q + 8 q^{9} + 8 q^{11} - 8 q^{12} - 16 q^{14} - 24 q^{15} + 360 q^{16} + 24 q^{18} - 16 q^{19} - 16 q^{22} + 32 q^{23} - 8 q^{24} - 24 q^{27} + 16 q^{29} - 32 q^{31} - 32 q^{33} + 32 q^{34} - 32 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{39} - 16 q^{41} + 32 q^{42} + 8 q^{43} + 16 q^{44} - 40 q^{45} - 32 q^{46} - 48 q^{49} - 488 q^{50} + 16 q^{52} + 16 q^{53} + 804 q^{54} - 16 q^{57} + 4 q^{59} - 672 q^{60} - 16 q^{61} - 24 q^{63} + 64 q^{65} + 24 q^{66} - 448 q^{67} + 64 q^{69} + 416 q^{71} + 64 q^{73} - 32 q^{75} + 16 q^{76} - 32 q^{77} + 16 q^{79} + 24 q^{82} - 8 q^{83} - 96 q^{85} - 16 q^{87} + 24 q^{88} + 32 q^{91} + 16 q^{92} - 128 q^{93} - 32 q^{94} + 24 q^{97} - 396 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2006, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2006, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2006, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 2}\)