Properties

Label 2009.2.bl
Level $2009$
Weight $2$
Character orbit 2009.bl
Rep. character $\chi_{2009}(81,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2328$
Sturm bound $392$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bl (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(392\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2009, [\chi])\).

Total New Old
Modular forms 2376 2376 0
Cusp forms 2328 2328 0
Eisenstein series 48 48 0

Trace form

\( 2328q - 26q^{2} + 166q^{4} - 22q^{5} - 16q^{8} - 184q^{9} + O(q^{10}) \) \( 2328q - 26q^{2} + 166q^{4} - 22q^{5} - 16q^{8} - 184q^{9} - 44q^{10} + 166q^{16} - 26q^{18} - 44q^{20} + 20q^{21} - 74q^{23} + 160q^{25} + 64q^{31} - 112q^{32} - 8q^{33} + 464q^{36} - 12q^{37} - 42q^{39} - 72q^{40} - 10q^{41} - 82q^{42} - 20q^{43} - 68q^{45} + 128q^{46} + 68q^{49} - 48q^{50} + 96q^{51} - 36q^{57} - 114q^{59} - 42q^{61} + 20q^{62} - 344q^{64} - 80q^{66} + 274q^{72} + 30q^{73} - 64q^{74} - 38q^{77} + 44q^{78} - 200q^{80} + 358q^{81} + 28q^{82} - 56q^{83} - 268q^{84} + 64q^{86} - 234q^{87} - 224q^{90} + 250q^{91} - 132q^{92} - 22q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2009, [\chi])\) into newform subspaces

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