Properties

Label 176.2.e
Level $176$
Weight $2$
Character orbit 176.e
Rep. character $\chi_{176}(175,\cdot)$
Character field $\Q$
Dimension $6$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
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 30 6 24
Cusp forms 18 6 12
Eisenstein series 12 0 12

Trace form

\( 6 q - 18 q^{9} + O(q^{10}) \) \( 6 q - 18 q^{9} + 30 q^{25} - 12 q^{45} - 42 q^{49} + 36 q^{53} - 60 q^{69} + 54 q^{81} + 84 q^{93} + O(q^{100}) \)

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.e.a 176.e 44.c $2$ $1.405$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}+3q^{5}-8q^{9}+\beta q^{11}-3\beta q^{15}+\cdots\)
176.2.e.b 176.e 44.c $4$ $1.405$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots\)

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

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