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Properties

Label 84.9.g
Level $84$
Weight $9$
Character orbit 84.g
Rep. character $\chi_{84}(43,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 132 48 84
Cusp forms 124 48 76
Eisenstein series 8 0 8

Trace form

\( 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9} + O(q^{10}) \) \( 48 q - 6 q^{2} + 290 q^{4} + 672 q^{5} - 2268 q^{6} + 4230 q^{8} - 104976 q^{9} - 41972 q^{10} + 22680 q^{12} + 57120 q^{13} - 14406 q^{14} - 207950 q^{16} + 386400 q^{17} + 13122 q^{18} + 562380 q^{20} + 1186136 q^{22} + 74844 q^{24} + 5520720 q^{25} + 1682100 q^{26} + 148862 q^{28} - 1994592 q^{29} - 2054808 q^{30} + 7754814 q^{32} + 2395820 q^{34} - 634230 q^{36} - 5931232 q^{37} - 4284000 q^{38} - 16076956 q^{40} + 10936800 q^{41} + 12531912 q^{44} - 1469664 q^{45} + 9456072 q^{46} - 12365136 q^{48} - 39530064 q^{49} - 6199074 q^{50} - 6937420 q^{52} - 7150560 q^{53} + 4960116 q^{54} + 14218722 q^{56} + 518452 q^{58} + 3633984 q^{60} - 42829024 q^{61} - 93291072 q^{62} - 69128614 q^{64} + 21653184 q^{65} + 45582264 q^{66} + 82618620 q^{68} + 17273088 q^{69} - 11611236 q^{70} - 9251010 q^{72} - 49489440 q^{73} - 126365628 q^{74} - 223942320 q^{76} + 94964352 q^{77} + 136267920 q^{78} + 238226604 q^{80} + 229582512 q^{81} + 269696252 q^{82} + 301906816 q^{85} - 188004816 q^{86} - 116561288 q^{88} - 315415968 q^{89} + 91792764 q^{90} + 487386984 q^{92} + 37454400 q^{93} + 148324176 q^{94} - 320488812 q^{96} - 3460128 q^{97} + 4941258 q^{98} + O(q^{100}) \)

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.g.a 84.g 4.b $48$ $34.220$ None \(-6\) \(0\) \(672\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(84, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)