Properties

Label 176.9.h
Level $176$
Weight $9$
Character orbit 176.h
Rep. character $\chi_{176}(65,\cdot)$
Character field $\Q$
Dimension $47$
Newform subspaces $6$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 176.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(176, [\chi])\).

Total New Old
Modular forms 198 49 149
Cusp forms 186 47 139
Eisenstein series 12 2 10

Trace form

\( 47 q + 2 q^{3} - 2 q^{5} + 102221 q^{9} + O(q^{10}) \) \( 47 q + 2 q^{3} - 2 q^{5} + 102221 q^{9} + 9889 q^{11} + 98468 q^{15} + 650306 q^{23} + 2721997 q^{25} + 664964 q^{27} + 2 q^{31} - 644930 q^{33} + 2360254 q^{37} - 794374 q^{45} - 667294 q^{47} - 30146577 q^{49} + 5131390 q^{53} + 13359874 q^{55} - 9739774 q^{59} + 101498562 q^{67} - 36178116 q^{69} + 4502402 q^{71} - 12266618 q^{75} + 21892992 q^{77} + 188723691 q^{81} + 6166270 q^{89} - 241880448 q^{91} - 211173444 q^{93} + 36754046 q^{97} + 206261891 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.9.h.a 176.h 11.b $1$ $71.699$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(113\) \(1151\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+113q^{3}+1151q^{5}+6208q^{9}-11^{4}q^{11}+\cdots\)
176.9.h.b 176.h 11.b $2$ $71.699$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-113\) \(-1151\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-59-5\beta )q^{3}+(-565+21\beta )q^{5}+\cdots\)
176.9.h.c 176.h 11.b $6$ $71.699$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(36\) \(-448\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(6+\beta _{5})q^{3}+(-73-5\beta _{4}-3\beta _{5})q^{5}+\cdots\)
176.9.h.d 176.h 11.b $6$ $71.699$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(36\) \(1856\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(6+\beta _{2})q^{3}+(309+\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)
176.9.h.e 176.h 11.b $8$ $71.699$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-182\) \(-1410\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-23-\beta _{1})q^{3}+(-176+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
176.9.h.f 176.h 11.b $24$ $71.699$ None \(0\) \(112\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)