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Properties

Label 84.9.h
Level $84$
Weight $9$
Character orbit 84.h
Rep. character $\chi_{84}(83,\cdot)$
Character field $\Q$
Dimension $124$
Newform subspaces $5$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(84, [\chi])\).

Total New Old
Modular forms 132 132 0
Cusp forms 124 124 0
Eisenstein series 8 8 0

Trace form

\( 124 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 124 q - 4 q^{4} - 4 q^{9} - 111356 q^{16} - 289340 q^{18} + 157724 q^{21} - 916944 q^{22} + 7800116 q^{25} + 54500 q^{28} - 1786676 q^{30} - 4508704 q^{36} + 4288952 q^{37} - 8996308 q^{42} + 6930904 q^{46} + 9484540 q^{49} - 9885768 q^{57} - 18533288 q^{58} - 24117668 q^{60} - 32389444 q^{64} - 3664664 q^{70} + 76835716 q^{72} - 13132860 q^{78} + 195701756 q^{81} + 28052356 q^{84} - 37934544 q^{85} + 114098480 q^{88} + 136225272 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.9.h.a 84.h 84.h $1$ $34.220$ \(\Q\) \(\Q(\sqrt{-21}) \) \(-16\) \(-81\) \(-94\) \(-2401\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-94q^{5}+\cdots\)
84.9.h.b 84.h 84.h $1$ $34.220$ \(\Q\) \(\Q(\sqrt{-21}) \) \(-16\) \(81\) \(94\) \(2401\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+94q^{5}+\cdots\)
84.9.h.c 84.h 84.h $1$ $34.220$ \(\Q\) \(\Q(\sqrt{-21}) \) \(16\) \(-81\) \(94\) \(-2401\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}+94q^{5}+\cdots\)
84.9.h.d 84.h 84.h $1$ $34.220$ \(\Q\) \(\Q(\sqrt{-21}) \) \(16\) \(81\) \(-94\) \(2401\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}-94q^{5}+\cdots\)
84.9.h.e 84.h 84.h $120$ $34.220$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$