Properties

Label 120.2.d
Level $120$
Weight $2$
Character orbit 120.d
Rep. character $\chi_{120}(109,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 28 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

Trace form

\( 12q + 2q^{4} - 2q^{6} + 12q^{9} + O(q^{10}) \) \( 12q + 2q^{4} - 2q^{6} + 12q^{9} - 10q^{10} - 20q^{14} + 2q^{16} - 4q^{20} - 2q^{24} + 4q^{25} - 28q^{26} + 12q^{30} - 32q^{31} + 24q^{34} + 2q^{36} - 16q^{39} + 22q^{40} - 8q^{41} + 44q^{44} - 4q^{46} - 12q^{49} - 2q^{54} - 16q^{55} + 52q^{56} - 22q^{60} - 46q^{64} - 24q^{65} + 20q^{66} + 32q^{70} + 32q^{71} + 36q^{74} + 12q^{76} + 32q^{79} - 12q^{80} + 12q^{81} - 4q^{84} + 40q^{86} - 40q^{89} - 10q^{90} - 4q^{94} + 64q^{95} - 42q^{96} + O(q^{100}) \)

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.d.a \(6\) \(0.958\) 6.0.839056.1 None \(-1\) \(6\) \(0\) \(0\) \(q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
120.2.d.b \(6\) \(0.958\) 6.0.839056.1 None \(1\) \(-6\) \(0\) \(0\) \(q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)