Properties

Label 176.2.q
Level $176$
Weight $2$
Character orbit 176.q
Rep. character $\chi_{176}(63,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 176.q (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 120 24 96
Cusp forms 72 24 48
Eisenstein series 48 0 48

Trace form

\( 24 q + 18 q^{9} + O(q^{10}) \) \( 24 q + 18 q^{9} - 30 q^{25} - 30 q^{33} - 60 q^{41} - 48 q^{45} - 18 q^{49} - 36 q^{53} - 30 q^{57} + 60 q^{69} + 60 q^{73} + 60 q^{77} + 36 q^{81} + 120 q^{85} + 60 q^{89} + 36 q^{93} + 90 q^{97} + O(q^{100}) \)

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.q.a 176.q 44.g $8$ $1.405$ 8.0.484000000.6 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{3}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
176.2.q.b 176.q 44.g $16$ $1.405$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{2}+\beta _{4}-\beta _{6}-\beta _{9}+\beta _{11})q^{3}+(1+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)