Properties

Label 36.9.c
Level $36$
Weight $9$
Character orbit 36.c
Rep. character $\chi_{36}(17,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 36.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(36, [\chi])\).

Total New Old
Modular forms 54 2 52
Cusp forms 42 2 40
Eisenstein series 12 0 12

Trace form

\( 2 q + 616 q^{7} + O(q^{10}) \) \( 2 q + 616 q^{7} + 36928 q^{13} + 299104 q^{19} + 778334 q^{25} + 933064 q^{31} - 1929044 q^{37} - 4134320 q^{43} - 11339874 q^{49} - 711504 q^{55} - 7532780 q^{61} + 52447024 q^{67} + 1418272 q^{73} + 76931320 q^{79} - 9060012 q^{85} + 11373824 q^{91} - 222541376 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.9.c.a 36.c 3.b $2$ $14.666$ \(\Q(\sqrt{-2}) \) None 36.9.c.a \(0\) \(0\) \(0\) \(616\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+308q^{7}+244\beta q^{11}+18464q^{13}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)