Properties

Label 120.2.m
Level $120$
Weight $2$
Character orbit 120.m
Rep. character $\chi_{120}(59,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(120, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 20q - 2q^{4} - 6q^{6} - 4q^{9} + 6q^{10} - 14q^{16} - 16q^{19} - 14q^{24} - 4q^{25} + 16q^{30} - 8q^{34} - 38q^{36} + 22q^{40} + 40q^{46} - 12q^{49} - 16q^{51} + 14q^{54} + 30q^{60} + 22q^{64} + 64q^{66} - 64q^{70} + 32q^{75} + 56q^{76} - 12q^{81} + 32q^{84} - 46q^{90} - 64q^{91} - 40q^{94} + 70q^{96} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
120.2.m.a \(4\) \(0.958\) \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
120.2.m.b \(16\) \(0.958\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{13}q^{3}-\beta _{11}q^{4}+\beta _{7}q^{5}+\cdots\)