Properties

Label 135.3.i
Level $135$
Weight $3$
Character orbit 135.i
Rep. character $\chi_{135}(71,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 135.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(135, [\chi])\).

Total New Old
Modular forms 84 16 68
Cusp forms 60 16 44
Eisenstein series 24 0 24

Trace form

\( 16 q + 16 q^{4} + 2 q^{7} + O(q^{10}) \) \( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.3.i.a 135.i 9.d $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+2\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)