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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.3.u.a 120.u 5.c $4$ $3.270$ \(\Q(i, \sqrt{6})\) None 120.3.u.a \(0\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(1+\beta _{1}+3\beta _{2}-2\beta _{3})q^{5}+\cdots\)
120.3.u.b 120.u 5.c $8$ $3.270$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 120.3.u.b \(0\) \(0\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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