Properties

Label 24.8.f
Level 24
Weight 8
Character orbit f
Rep. character \(\chi_{24}(11,\cdot)\)
Character field \(\Q\)
Dimension 26
Newforms 3
Sturm bound 32
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(24, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

Trace form

\( 26q - 2q^{3} - 28q^{4} + 40q^{6} - 2q^{9} + O(q^{10}) \) \( 26q - 2q^{3} - 28q^{4} + 40q^{6} - 2q^{9} - 5304q^{10} - 12812q^{12} - 14872q^{16} - 9800q^{18} + 60580q^{19} - 82496q^{22} - 81080q^{24} + 281246q^{25} + 238042q^{27} - 50352q^{28} - 24624q^{30} - 45136q^{33} - 332816q^{34} - 148244q^{36} + 115872q^{40} + 331272q^{42} - 752852q^{43} + 378144q^{46} + 566200q^{48} - 2158138q^{49} - 1112848q^{51} + 1542144q^{52} + 26104q^{54} - 347548q^{57} + 2501160q^{58} + 414000q^{60} - 728272q^{64} - 91288q^{66} + 1552540q^{67} + 5522736q^{70} + 3503824q^{72} + 1267060q^{73} + 573562q^{75} - 213032q^{76} - 10346544q^{78} + 6421738q^{81} - 17006144q^{82} - 12156480q^{84} - 17283152q^{88} + 14281704q^{90} + 4997664q^{91} - 2342208q^{94} + 7955728q^{96} + 13155724q^{97} + 14430800q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(24, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.8.f.a \(2\) \(7.497\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-86\) \(0\) \(0\) \(q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots\)
24.8.f.b \(4\) \(7.497\) \(\Q(\sqrt{6}, \sqrt{-26})\) None \(0\) \(-36\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots\)
24.8.f.c \(20\) \(7.497\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(120\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots\)