Properties

Label 176.2.j
Level $176$
Weight $2$
Character orbit 176.j
Rep. character $\chi_{176}(45,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
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 52 40 12
Cusp forms 44 40 4
Eisenstein series 8 0 8

Trace form

\( 40 q - 12 q^{6} - 12 q^{8} + O(q^{10}) \) \( 40 q - 12 q^{6} - 12 q^{8} - 4 q^{10} - 12 q^{12} + 8 q^{14} - 16 q^{15} - 8 q^{16} - 20 q^{18} - 16 q^{19} - 20 q^{20} + 28 q^{24} + 24 q^{27} + 20 q^{28} + 12 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 20 q^{36} + 48 q^{38} - 8 q^{40} - 8 q^{44} - 52 q^{46} - 40 q^{47} - 40 q^{49} + 64 q^{50} - 24 q^{51} - 36 q^{52} + 32 q^{54} - 8 q^{56} + 40 q^{58} - 8 q^{59} + 12 q^{60} + 32 q^{61} - 24 q^{64} - 16 q^{65} - 20 q^{66} - 24 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 20 q^{72} - 56 q^{74} - 56 q^{75} + 4 q^{76} + 64 q^{78} + 32 q^{79} + 32 q^{80} - 40 q^{81} + 24 q^{82} + 40 q^{83} + 76 q^{84} - 32 q^{85} - 16 q^{86} + 20 q^{90} - 16 q^{91} + 12 q^{92} - 48 q^{93} + 16 q^{94} - 48 q^{95} + 36 q^{96} + 72 q^{98} + O(q^{100}) \)

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.j.a 176.j 16.e $40$ $1.405$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)