Properties

Label 176.2.x
Level $176$
Weight $2$
Character orbit 176.x
Rep. character $\chi_{176}(19,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $176$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 176.x (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(176, [\chi])\).

Total New Old
Modular forms 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176 q - 10 q^{2} - 6 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{6} - 20 q^{7} - 10 q^{8} + O(q^{10}) \) \( 176 q - 10 q^{2} - 6 q^{3} - 10 q^{4} - 6 q^{5} - 10 q^{6} - 20 q^{7} - 10 q^{8} - 4 q^{11} - 32 q^{12} - 10 q^{13} - 12 q^{14} + 14 q^{16} - 20 q^{17} + 40 q^{18} - 10 q^{19} - 14 q^{20} - 66 q^{22} - 16 q^{23} - 10 q^{24} + 56 q^{26} - 18 q^{27} - 10 q^{28} - 10 q^{29} - 50 q^{30} - 16 q^{33} - 4 q^{34} - 10 q^{35} - 22 q^{36} - 30 q^{37} + 22 q^{38} - 20 q^{39} - 10 q^{40} - 10 q^{42} - 46 q^{44} - 48 q^{45} - 30 q^{46} + 14 q^{48} + 8 q^{49} - 10 q^{50} - 10 q^{51} - 50 q^{52} + 18 q^{53} + 16 q^{55} + 8 q^{56} + 14 q^{58} + 10 q^{59} - 82 q^{60} - 10 q^{61} - 10 q^{62} + 38 q^{64} + 58 q^{66} - 56 q^{67} - 140 q^{68} - 24 q^{69} + 68 q^{70} + 20 q^{71} + 190 q^{72} + 40 q^{74} + 10 q^{75} - 14 q^{77} - 4 q^{78} + 148 q^{80} + 42 q^{82} - 110 q^{83} + 40 q^{84} - 10 q^{85} - 2 q^{86} + 182 q^{88} + 60 q^{90} + 54 q^{91} + 90 q^{92} - 18 q^{93} + 180 q^{94} + 90 q^{96} - 12 q^{97} - 68 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.2.x.a 176.x 176.x $176$ $1.405$ None \(-10\) \(-6\) \(-6\) \(-20\) $\mathrm{SU}(2)[C_{20}]$