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Properties

Label 18.7.b
Level $18$
Weight $7$
Character orbit 18.b
Rep. character $\chi_{18}(17,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 18.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(18, [\chi])\).

Total New Old
Modular forms 22 2 20
Cusp forms 14 2 12
Eisenstein series 8 0 8

Trace form

\( 2 q - 64 q^{4} - 968 q^{7} + O(q^{10}) \) \( 2 q - 64 q^{4} - 968 q^{7} - 1968 q^{10} + 6736 q^{13} + 2048 q^{16} + 11488 q^{19} - 15168 q^{22} - 29266 q^{25} + 30976 q^{28} - 79592 q^{31} - 144 q^{34} + 105052 q^{37} + 62976 q^{40} + 7600 q^{43} + 38208 q^{46} + 233214 q^{49} - 215552 q^{52} - 466416 q^{55} - 332112 q^{58} + 26500 q^{61} - 65536 q^{64} + 337936 q^{67} + 952512 q^{70} + 472288 q^{73} - 367616 q^{76} - 70232 q^{79} + 419088 q^{82} - 4428 q^{85} + 485376 q^{88} - 3260224 q^{91} - 868800 q^{94} - 642848 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(18, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.7.b.a 18.b 3.b $2$ $4.141$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-968\) $\mathrm{SU}(2)[C_{2}]$ \(q+4\beta q^{2}-2^{5}q^{4}+123\beta q^{5}-22^{2}q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)