↑

Properties

Label 2006.2.j
Level $2006$
Weight $2$
Character orbit 2006.j
Rep. character $\chi_{2006}(235,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $720$
Sturm bound $540$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2006.j (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2192 720 1472
Cusp forms 2128 720 1408
Eisenstein series 64 0 64

Trace form

\( 720 q + O(q^{10}) \) \( 720 q - 16 q^{12} + 48 q^{15} + 32 q^{17} - 32 q^{19} - 48 q^{21} - 32 q^{22} + 48 q^{27} - 64 q^{35} - 96 q^{41} - 128 q^{45} + 64 q^{46} - 128 q^{49} + 176 q^{57} + 80 q^{59} + 144 q^{63} - 16 q^{66} - 32 q^{71} - 80 q^{75} + 128 q^{78} + 96 q^{79} - 16 q^{81} + 192 q^{85} + 288 q^{87} + 128 q^{94} - 128 q^{95} + O(q^{100}) \)

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

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