Properties

Label 120.3.c
Level $120$
Weight $3$
Character orbit 120.c
Rep. character $\chi_{120}(89,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 120.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(120, [\chi])\).

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12q + 8q^{9} + O(q^{10}) \) \( 12q + 8q^{9} + 16q^{15} + 4q^{21} + 36q^{25} - 48q^{31} - 128q^{39} - 68q^{45} - 252q^{49} + 48q^{51} - 48q^{55} + 144q^{61} + 268q^{69} + 304q^{75} + 432q^{79} - 188q^{81} + 336q^{85} - 560q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
120.3.c.a \(12\) \(3.270\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)