Properties

Label 138.3.c
Level $138$
Weight $3$
Character orbit 138.c
Rep. character $\chi_{138}(47,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 138.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(138, [\chi])\).

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16q + 4q^{3} - 32q^{4} - 8q^{6} - 4q^{9} + O(q^{10}) \) \( 16q + 4q^{3} - 32q^{4} - 8q^{6} - 4q^{9} - 8q^{12} - 8q^{13} + 28q^{15} + 64q^{16} + 16q^{18} + 40q^{19} + 4q^{21} + 16q^{22} + 16q^{24} - 192q^{25} - 80q^{27} - 24q^{30} + 136q^{31} - 84q^{33} - 16q^{34} + 8q^{36} - 136q^{37} + 156q^{39} + 128q^{42} + 72q^{43} + 4q^{45} + 16q^{48} + 224q^{49} - 4q^{51} + 16q^{52} - 176q^{54} - 96q^{55} - 160q^{57} - 56q^{60} + 48q^{61} + 204q^{63} - 128q^{64} - 144q^{66} - 304q^{67} - 176q^{70} - 32q^{72} + 408q^{73} + 68q^{75} - 80q^{76} + 328q^{78} + 312q^{79} + 164q^{81} + 160q^{82} - 8q^{84} - 464q^{85} - 268q^{87} - 32q^{88} + 32q^{90} - 72q^{91} - 108q^{93} - 32q^{96} + 168q^{97} - 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
138.3.c.a \(16\) \(3.760\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{7}q^{5}+\beta _{11}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)