Properties

Label 154.2.n
Level $154$
Weight $2$
Character orbit 154.n
Rep. character $\chi_{154}(17,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $64$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.n (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(154, [\chi])\).

Total New Old
Modular forms 224 64 160
Cusp forms 160 64 96
Eisenstein series 64 0 64

Trace form

\( 64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9} + O(q^{10}) \) \( 64 q - 8 q^{4} + 12 q^{5} - 10 q^{7} + 4 q^{9} - 8 q^{11} - 2 q^{14} - 12 q^{15} + 8 q^{16} - 30 q^{17} + 8 q^{22} - 16 q^{23} - 20 q^{25} - 24 q^{26} + 10 q^{28} + 20 q^{29} - 18 q^{31} - 126 q^{33} + 30 q^{35} - 32 q^{36} + 16 q^{37} - 12 q^{38} + 20 q^{39} - 30 q^{40} - 2 q^{42} - 2 q^{44} + 108 q^{45} - 24 q^{47} - 78 q^{49} - 60 q^{51} + 8 q^{53} + 4 q^{56} - 80 q^{57} - 28 q^{58} - 60 q^{59} + 4 q^{60} + 30 q^{61} + 50 q^{63} + 16 q^{64} + 72 q^{66} - 32 q^{67} + 30 q^{68} - 10 q^{70} - 8 q^{71} + 20 q^{72} + 90 q^{73} + 20 q^{74} + 180 q^{75} + 46 q^{77} + 96 q^{78} + 30 q^{79} + 18 q^{80} + 48 q^{81} + 60 q^{82} + 40 q^{84} + 140 q^{85} + 10 q^{86} + 14 q^{88} - 36 q^{89} + 106 q^{91} + 28 q^{92} + 94 q^{93} - 120 q^{94} - 70 q^{95} + 104 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(154, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.2.n.a 154.n 77.n $64$ $1.230$ None 154.2.n.a \(0\) \(0\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(154, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)