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Properties

Label 120.4.w
Level $120$
Weight $4$
Character orbit 120.w
Rep. character $\chi_{120}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $136$
Newform subspaces $3$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(120, [\chi])\).

Total New Old
Modular forms 152 152 0
Cusp forms 136 136 0
Eisenstein series 16 16 0

Trace form

\( 136 q - 4 q^{6} - 8 q^{7} + 68 q^{10} - 56 q^{12} - 4 q^{15} + 124 q^{16} + 220 q^{18} - 252 q^{22} - 8 q^{25} - 180 q^{28} + 328 q^{30} - 544 q^{31} - 112 q^{33} + 460 q^{36} - 136 q^{40} - 536 q^{42}+ \cdots - 1496 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
120.4.w.a 120.w 120.w $4$ $7.080$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) 120.4.w.a \(-8\) \(0\) \(-28\) \(68\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
120.4.w.b 120.w 120.w $4$ $7.080$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) 120.4.w.a \(8\) \(0\) \(28\) \(68\) $\mathrm{U}(1)[D_{4}]$ \(q+(2-2\beta _{2})q^{2}+\beta _{1}q^{3}-8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots\)
120.4.w.c 120.w 120.w $128$ $7.080$ None 120.4.w.c \(0\) \(0\) \(0\) \(-144\) $\mathrm{SU}(2)[C_{4}]$