Properties

Label 54.9.b
Level $54$
Weight $9$
Character orbit 54.b
Rep. character $\chi_{54}(53,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $81$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(81\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(54, [\chi])\).

Total New Old
Modular forms 78 10 68
Cusp forms 66 10 56
Eisenstein series 12 0 12

Trace form

\( 10 q - 1280 q^{4} - 3658 q^{7} + O(q^{10}) \) \( 10 q - 1280 q^{4} - 3658 q^{7} + 8448 q^{10} + 71090 q^{13} + 163840 q^{16} + 2306 q^{19} - 384000 q^{22} + 230182 q^{25} + 468224 q^{28} - 127144 q^{31} - 3884544 q^{34} + 6875498 q^{37} - 1081344 q^{40} - 23144764 q^{43} + 6300672 q^{46} + 14456352 q^{49} - 9099520 q^{52} + 63437004 q^{55} - 20659200 q^{58} + 11655626 q^{61} - 20971520 q^{64} - 15060070 q^{67} - 70411776 q^{70} - 10846114 q^{73} - 295168 q^{76} + 26971610 q^{79} + 26995200 q^{82} + 123210072 q^{85} + 49152000 q^{88} - 160865834 q^{91} - 290075136 q^{94} + 57846470 q^{97} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.9.b.a 54.b 3.b $2$ $21.998$ \(\Q(\sqrt{-2}) \) None 54.9.b.a \(0\) \(0\) \(0\) \(-4130\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2^{7}q^{4}+60\beta q^{5}-2065q^{7}+\cdots\)
54.9.b.b 54.b 3.b $4$ $21.998$ \(\Q(\sqrt{-2}, \sqrt{79})\) None 54.9.b.b \(0\) \(0\) \(0\) \(164\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-2^{7}q^{4}+(-21\beta _{1}+\beta _{2})q^{5}+\cdots\)
54.9.b.c 54.b 3.b $4$ $21.998$ \(\Q(\zeta_{8})\) None 54.9.b.c \(0\) \(0\) \(0\) \(308\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{8}^{2}q^{2}-2^{7}q^{4}+(-11\zeta_{8}+51\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(54, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)