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Properties

Label 120.4.k
Level $120$
Weight $4$
Character orbit 120.k
Rep. character $\chi_{120}(61,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
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.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 24 52
Cusp forms 68 24 44
Eisenstein series 8 0 8

Trace form

\( 24 q - 4 q^{2} - 26 q^{4} + 6 q^{6} - 56 q^{7} + 68 q^{8} - 216 q^{9} + O(q^{10}) \) \( 24 q - 4 q^{2} - 26 q^{4} + 6 q^{6} - 56 q^{7} + 68 q^{8} - 216 q^{9} - 30 q^{10} - 36 q^{14} + 60 q^{15} - 62 q^{16} + 36 q^{18} - 40 q^{20} + 28 q^{22} - 656 q^{23} - 294 q^{24} - 600 q^{25} - 316 q^{26} + 500 q^{28} + 264 q^{31} + 836 q^{32} + 816 q^{34} + 234 q^{36} - 480 q^{38} - 30 q^{40} + 468 q^{42} - 1188 q^{44} + 412 q^{46} - 624 q^{48} + 456 q^{49} + 100 q^{50} + 184 q^{52} - 54 q^{54} - 880 q^{55} + 3772 q^{56} + 336 q^{57} + 1452 q^{58} + 330 q^{60} + 1608 q^{62} + 504 q^{63} + 742 q^{64} + 924 q^{66} - 1520 q^{68} - 1780 q^{70} + 3184 q^{71} - 612 q^{72} - 432 q^{73} - 2996 q^{74} - 1092 q^{76} - 3144 q^{78} - 1656 q^{79} - 880 q^{80} + 1944 q^{81} + 2032 q^{82} + 1764 q^{84} + 3000 q^{86} - 2088 q^{87} - 5508 q^{88} + 270 q^{90} - 2904 q^{92} - 3068 q^{94} + 126 q^{96} + 1584 q^{97} + 2892 q^{98} + O(q^{100}) \)

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.k.a 120.k 8.b $2$ $7.080$ \(\Q(\sqrt{-1}) \) None 120.4.k.a \(-4\) \(0\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+2i)q^{2}+3iq^{3}-8iq^{4}+5iq^{5}+\cdots\)
120.4.k.b 120.k 8.b $8$ $7.080$ 8.0.\(\cdots\).4 None 120.4.k.b \(2\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+3\beta _{2}q^{3}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
120.4.k.c 120.k 8.b $14$ $7.080$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 120.4.k.c \(-2\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+3\beta _{3}q^{3}-\beta _{2}q^{4}-5\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(120, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)