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Properties

Label 6.9.b
Level $6$
Weight $9$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(6, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

Trace form

\( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9} + O(q^{10}) \) \( 2 q - 126 q^{3} - 256 q^{4} - 1152 q^{6} + 5572 q^{7} + 2754 q^{9} - 13056 q^{10} + 16128 q^{12} - 26300 q^{13} - 58752 q^{15} + 32768 q^{16} + 145152 q^{18} + 288004 q^{19} - 351036 q^{21} - 507648 q^{22} + 147456 q^{24} + 115394 q^{25} + 479682 q^{27} - 713216 q^{28} + 822528 q^{30} + 1457476 q^{31} - 2284416 q^{33} + 1502208 q^{34} - 352512 q^{36} - 3928892 q^{37} + 1656900 q^{39} + 1671168 q^{40} - 3209472 q^{42} - 156284 q^{43} + 7402752 q^{45} - 1116672 q^{46} - 2064384 q^{48} + 3993990 q^{49} + 6759936 q^{51} + 3366400 q^{52} - 10730880 q^{54} - 25890048 q^{55} - 18144252 q^{57} + 14196480 q^{58} + 7520256 q^{60} + 35156548 q^{61} + 7672644 q^{63} - 4194304 q^{64} + 31981824 q^{66} - 34273532 q^{67} - 5025024 q^{69} - 36374016 q^{70} - 18579456 q^{72} + 56278660 q^{73} - 7269822 q^{75} - 36864512 q^{76} + 15148800 q^{78} + 18364996 q^{79} - 78508926 q^{81} - 22313472 q^{82} + 44932608 q^{84} + 76612608 q^{85} + 63884160 q^{87} + 64978944 q^{88} - 17978112 q^{90} - 73271800 q^{91} - 91820988 q^{93} + 79641600 q^{94} - 18874368 q^{96} - 257445116 q^{97} + 287836416 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.9.b.a 6.b 3.b $2$ $2.444$ \(\Q(\sqrt{-2}) \) None \(0\) \(-126\) \(0\) \(5572\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)