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Properties

Label 118.2.c
Level $118$
Weight $2$
Character orbit 118.c
Rep. character $\chi_{118}(3,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $140$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 118 = 2 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 118.c (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(118, [\chi])\).

Total New Old
Modular forms 476 140 336
Cusp forms 364 140 224
Eisenstein series 112 0 112

Trace form

\( 140 q - q^{2} - 6 q^{3} - 5 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - q^{8} - 11 q^{9} + O(q^{10}) \) \( 140 q - q^{2} - 6 q^{3} - 5 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - q^{8} - 11 q^{9} - 6 q^{10} - 12 q^{11} - 6 q^{12} - 6 q^{13} - 12 q^{14} - 26 q^{15} - 5 q^{16} - 20 q^{17} - 13 q^{18} - 14 q^{19} - 4 q^{20} - 18 q^{21} - 14 q^{22} - 40 q^{23} - 4 q^{24} - 29 q^{25} - 4 q^{26} - 42 q^{27} - 4 q^{28} - 24 q^{29} - 12 q^{30} - 36 q^{31} - q^{32} - 48 q^{33} - 26 q^{34} - 54 q^{35} - 11 q^{36} - 26 q^{37} - 24 q^{38} - 64 q^{39} - 6 q^{40} - 50 q^{41} - 28 q^{42} - 32 q^{43} - 12 q^{44} - 24 q^{45} + 34 q^{46} + 6 q^{47} - 6 q^{48} + 59 q^{49} + 93 q^{50} + 144 q^{51} + 52 q^{52} + 52 q^{53} + 163 q^{54} + 90 q^{55} - 12 q^{56} + 216 q^{57} + 24 q^{58} + 59 q^{59} + 148 q^{60} + 66 q^{61} + 34 q^{62} + 196 q^{63} - 5 q^{64} + 78 q^{65} + 163 q^{66} + 32 q^{67} + 38 q^{68} + 116 q^{69} + 56 q^{70} + 34 q^{71} - 13 q^{72} - 28 q^{73} + 6 q^{74} - 62 q^{75} - 14 q^{76} - 104 q^{77} - 48 q^{78} - 92 q^{79} - 4 q^{80} - 101 q^{81} - 26 q^{82} - 60 q^{83} - 18 q^{84} - 96 q^{85} - 62 q^{86} - 126 q^{87} - 14 q^{88} - 106 q^{89} - 66 q^{90} - 96 q^{91} - 40 q^{92} - 100 q^{93} - 60 q^{94} - 82 q^{95} - 4 q^{96} - 122 q^{97} - 65 q^{98} - 69 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(118, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
118.2.c.a 118.c 59.c $56$ $0.942$ None \(2\) \(-1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{29}]$
118.2.c.b 118.c 59.c $84$ $0.942$ None \(-3\) \(-5\) \(-5\) \(-8\) $\mathrm{SU}(2)[C_{29}]$

Decomposition of \(S_{2}^{\mathrm{old}}(118, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(118, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)