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Properties

Label 135.3.g
Level $135$
Weight $3$
Character orbit 135.g
Rep. character $\chi_{135}(28,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $2$
Sturm bound $54$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 135.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 84 32 52
Cusp forms 60 32 28
Eisenstein series 24 0 24

Trace form

\( 32 q + 8 q^{7} + O(q^{10}) \) \( 32 q + 8 q^{7} + 8 q^{10} + 68 q^{13} - 172 q^{16} + 40 q^{22} + 32 q^{25} - 32 q^{28} - 8 q^{31} - 160 q^{37} - 300 q^{40} - 52 q^{43} + 340 q^{46} + 452 q^{52} + 112 q^{55} + 552 q^{58} + 16 q^{61} - 40 q^{67} - 12 q^{70} - 832 q^{73} - 588 q^{76} - 956 q^{82} - 964 q^{85} + 72 q^{88} + 352 q^{91} + 164 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.g.a 135.g 5.c $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{4}+\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots\)
135.3.g.b 135.g 5.c $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{4})q^{4}+\beta _{10}q^{5}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(135, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)