Properties

Label 24.2.f
Level 24
Weight 2
Character orbit f
Rep. character \(\chi_{24}(11,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 8
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(24, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 16q^{64} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut +\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 14q^{81} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut +\mathstrut 16q^{88} \) \(\mathstrut +\mathstrut 16q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.2.f.a \(2\) \(0.192\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)