Properties

Label 96.2.f
Level 96
Weight 2
Character orbit f
Rep. character \(\chi_{96}(47,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 32
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 96.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

Trace form

\(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut +\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 14q^{81} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.2.f.a \(2\) \(0.767\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)