Properties

Label 2006.2.n
Level $2006$
Weight $2$
Character orbit 2006.n
Rep. character $\chi_{2006}(135,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2520$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2006.n (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 7672 2520 5152
Cusp forms 7448 2520 4928
Eisenstein series 224 0 224

Trace form

\( 2520 q + 2 q^{2} - 90 q^{4} + 2 q^{8} + 86 q^{9} + O(q^{10}) \) \( 2520 q + 2 q^{2} - 90 q^{4} + 2 q^{8} + 86 q^{9} - 12 q^{13} - 12 q^{15} - 90 q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{19} + 12 q^{21} + 90 q^{25} - 8 q^{30} + 2 q^{32} - 32 q^{33} - 22 q^{34} + 20 q^{35} + 86 q^{36} - 16 q^{38} + 16 q^{42} - 16 q^{43} - 124 q^{47} - 142 q^{49} + 94 q^{50} - 172 q^{51} + 104 q^{52} - 108 q^{53} + 16 q^{55} - 30 q^{59} + 336 q^{60} - 90 q^{64} - 398 q^{66} + 108 q^{67} - 54 q^{68} + 464 q^{69} - 68 q^{70} - 2 q^{72} + 4 q^{76} - 32 q^{77} - 18 q^{81} + 32 q^{83} + 12 q^{84} - 32 q^{85} + 12 q^{86} - 124 q^{87} - 36 q^{89} + 16 q^{93} - 24 q^{94} + 22 q^{98} + O(q^{100}) \)

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

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