Properties

Label 120.3.u
Level $120$
Weight $3$
Character orbit 120.u
Rep. character $\chi_{120}(73,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 120.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

Trace form

\( 12q - 8q^{5} - 8q^{7} + O(q^{10}) \) \( 12q - 8q^{5} - 8q^{7} + 16q^{11} + 44q^{13} + 24q^{15} + 28q^{17} - 96q^{23} - 68q^{25} + 16q^{31} + 72q^{33} + 52q^{37} - 208q^{41} - 96q^{43} - 36q^{45} - 32q^{47} - 12q^{53} + 136q^{55} - 96q^{57} + 240q^{61} - 24q^{63} + 20q^{65} - 224q^{67} + 32q^{71} - 100q^{73} + 96q^{75} + 240q^{77} - 108q^{81} + 608q^{83} + 60q^{85} + 360q^{87} + 256q^{91} + 144q^{93} - 32q^{95} - 356q^{97} + O(q^{100}) \)

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.u.a \(4\) \(3.270\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(-12\) \(q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots\)
120.3.u.b \(8\) \(3.270\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-12\) \(4\) \(q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)