Properties

Label 18.9.b
Level $18$
Weight $9$
Character orbit 18.b
Rep. character $\chi_{18}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $27$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 18.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(27\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(18, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 20 4 16
Eisenstein series 8 0 8

Trace form

\( 4 q - 512 q^{4} - 3760 q^{7} + O(q^{10}) \) \( 4 q - 512 q^{4} - 3760 q^{7} + 15360 q^{10} + 8960 q^{13} + 65536 q^{16} - 559936 q^{19} + 768000 q^{22} - 210500 q^{25} + 481280 q^{28} - 174064 q^{31} + 350208 q^{34} - 5020840 q^{37} - 1966080 q^{40} + 17916320 q^{43} - 12601344 q^{46} + 7349052 q^{49} - 1146880 q^{52} - 15691680 q^{55} + 814080 q^{58} - 6210520 q^{61} - 8388608 q^{64} + 49105760 q^{67} + 52746240 q^{70} - 121101760 q^{73} + 71671808 q^{76} + 11399024 q^{79} + 16005120 q^{82} - 245390040 q^{85} - 98304000 q^{88} + 448433152 q^{91} - 9922560 q^{94} - 62327680 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.9.b.a 18.b 3.b $2$ $7.333$ \(\Q(\sqrt{-2}) \) None 18.9.b.a \(0\) \(0\) \(0\) \(-7064\) $\mathrm{SU}(2)[C_{2}]$ \(q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots\)
18.9.b.b 18.b 3.b $2$ $7.333$ \(\Q(\sqrt{-2}) \) None 18.9.b.b \(0\) \(0\) \(0\) \(3304\) $\mathrm{SU}(2)[C_{2}]$ \(q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)