Properties

Label 24.3.h
Level $24$
Weight $3$
Character orbit 24.h
Rep. character $\chi_{24}(5,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $12$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 24.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} + O(q^{10}) \) \( 6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} - 24q^{10} + 28q^{12} - 20q^{15} + 40q^{16} + 56q^{18} + 64q^{22} - 88q^{24} - 14q^{25} - 128q^{28} - 112q^{30} + 60q^{31} - 12q^{33} - 112q^{34} + 132q^{36} + 112q^{39} + 128q^{40} + 136q^{42} + 224q^{46} - 168q^{48} - 30q^{49} - 112q^{52} - 184q^{54} - 232q^{55} + 56q^{57} - 152q^{58} + 144q^{60} - 260q^{63} + 272q^{64} + 168q^{66} + 16q^{70} - 112q^{72} + 76q^{73} - 56q^{76} - 112q^{78} + 380q^{79} + 38q^{81} - 224q^{82} + 112q^{84} + 396q^{87} - 80q^{88} + 8q^{90} - 16q^{96} + 92q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.h.a \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c \(4\) \(0.654\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)