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Properties

Label 176.2.i
Level $176$
Weight $2$
Character orbit 176.i
Rep. character $\chi_{176}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
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 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 4 q^{3} - 4 q^{5} + O(q^{10}) \) \( 44 q - 4 q^{3} - 4 q^{5} - 6 q^{11} + 12 q^{12} - 8 q^{14} - 24 q^{16} + 4 q^{20} - 4 q^{22} - 24 q^{23} - 16 q^{26} + 8 q^{27} - 4 q^{33} - 16 q^{34} + 12 q^{36} - 20 q^{37} - 32 q^{38} + 36 q^{44} + 28 q^{45} - 24 q^{48} - 28 q^{49} + 12 q^{53} - 36 q^{55} + 72 q^{56} - 24 q^{58} - 20 q^{59} - 68 q^{60} + 72 q^{64} - 68 q^{66} + 36 q^{67} - 16 q^{69} - 8 q^{70} - 40 q^{71} + 60 q^{75} + 4 q^{77} + 104 q^{78} + 32 q^{80} - 20 q^{81} + 48 q^{82} + 72 q^{86} - 32 q^{88} + 56 q^{91} - 60 q^{92} + 8 q^{93} - 8 q^{97} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.i.a 176.i 176.i $44$ $1.405$ None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$