Properties

Label 24.3.e
Level 24
Weight 3
Character orbit e
Rep. character \(\chi_{24}(17,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 4 2 2
Eisenstein series 8 0 8

Trace form

\(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 14q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 14q^{9} \) \(\mathstrut +\mathstrut 20q^{13} \) \(\mathstrut +\mathstrut 32q^{15} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{25} \) \(\mathstrut -\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 44q^{31} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 164q^{43} \) \(\mathstrut +\mathstrut 64q^{45} \) \(\mathstrut -\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 128q^{51} \) \(\mathstrut -\mathstrut 64q^{55} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 172q^{61} \) \(\mathstrut +\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut +\mathstrut 164q^{73} \) \(\mathstrut -\mathstrut 14q^{75} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 256q^{85} \) \(\mathstrut +\mathstrut 96q^{87} \) \(\mathstrut -\mathstrut 120q^{91} \) \(\mathstrut -\mathstrut 44q^{93} \) \(\mathstrut -\mathstrut 188q^{97} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.e.a \(2\) \(0.654\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)