Properties

Label 155.2.h
Level $155$
Weight $2$
Character orbit 155.h
Rep. character $\chi_{155}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $48$
Newform subspaces $2$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 155.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

Total New Old
Modular forms 72 48 24
Cusp forms 56 48 8
Eisenstein series 16 0 16

Trace form

\( 48 q - 4 q^{3} - 20 q^{4} - 16 q^{6} - 12 q^{7} + 18 q^{8} - 16 q^{9} + O(q^{10}) \) \( 48 q - 4 q^{3} - 20 q^{4} - 16 q^{6} - 12 q^{7} + 18 q^{8} - 16 q^{9} - 4 q^{10} + 6 q^{11} + 6 q^{12} - 18 q^{13} + 4 q^{14} - 4 q^{15} - 24 q^{16} - 28 q^{18} - 8 q^{20} - 4 q^{21} - 12 q^{22} - 26 q^{23} - 16 q^{24} + 48 q^{25} - 4 q^{26} - 22 q^{27} + 60 q^{28} - 2 q^{29} + 16 q^{30} + 8 q^{31} + 56 q^{32} + 14 q^{33} - 16 q^{34} + 6 q^{35} + 100 q^{36} - 20 q^{37} - 4 q^{38} - 12 q^{39} - 4 q^{40} - 12 q^{41} + 42 q^{42} + 16 q^{43} + 42 q^{44} - 4 q^{45} + 8 q^{46} - 24 q^{47} - 78 q^{48} - 38 q^{49} - 4 q^{51} - 50 q^{52} - 20 q^{53} + 2 q^{54} + 4 q^{55} - 104 q^{56} + 72 q^{57} + 92 q^{58} - 12 q^{59} - 30 q^{60} - 56 q^{61} + 102 q^{62} - 8 q^{63} + 34 q^{64} - 8 q^{65} - 92 q^{66} - 20 q^{67} + 92 q^{68} + 112 q^{69} - 8 q^{70} - 10 q^{71} - 94 q^{72} - 48 q^{73} - 42 q^{74} - 4 q^{75} - 34 q^{76} - 74 q^{77} - 42 q^{78} + 18 q^{79} + 24 q^{80} + 32 q^{81} + 40 q^{82} - 12 q^{83} + 54 q^{84} - 14 q^{85} - 44 q^{86} + 28 q^{87} - 84 q^{88} + 18 q^{89} + 8 q^{90} + 44 q^{91} + 68 q^{92} - 74 q^{93} - 108 q^{94} - 4 q^{95} + 34 q^{96} + 26 q^{97} - 144 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
155.2.h.a 155.h 31.d $24$ $1.238$ None \(-2\) \(-4\) \(24\) \(-3\) $\mathrm{SU}(2)[C_{5}]$
155.2.h.b 155.h 31.d $24$ $1.238$ None \(2\) \(0\) \(-24\) \(-9\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)