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Properties

Label 120.4.m
Level $120$
Weight $4$
Character orbit 120.m
Rep. character $\chi_{120}(59,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68 q - 10 q^{4} - 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 68 q - 10 q^{4} - 18 q^{6} - 4 q^{9} - 22 q^{10} - 142 q^{16} + 16 q^{19} - 254 q^{24} - 4 q^{25} - 248 q^{30} + 456 q^{34} - 14 q^{36} - 394 q^{40} - 104 q^{46} + 2148 q^{49} - 112 q^{51} + 506 q^{54} - 714 q^{60} + 614 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} - 1304 q^{76} + 612 q^{81} - 736 q^{84} - 82 q^{90} - 2752 q^{91} + 2056 q^{94} - 1034 q^{96} + 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.m.a 120.m 120.m $4$ $7.080$ \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) 120.4.m.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}+2\beta _{3})q^{3}+(6+\beta _{2}+\cdots)q^{4}+\cdots\)
120.4.m.b 120.m 120.m $64$ $7.080$ None 120.4.m.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$