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Properties

Label 135.2.f
Level $135$
Weight $2$
Character orbit 135.f
Rep. character $\chi_{135}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $2$
Sturm bound $36$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 135.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(135, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 24 16 8
Eisenstein series 24 0 24

Trace form

\( 16 q + 4 q^{7} + O(q^{10}) \) \( 16 q + 4 q^{7} + 4 q^{10} - 20 q^{13} - 20 q^{16} - 4 q^{22} - 8 q^{25} - 4 q^{28} + 8 q^{31} - 56 q^{37} + 60 q^{40} + 52 q^{43} - 28 q^{46} + 52 q^{52} - 4 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 120 q^{70} - 20 q^{73} + 36 q^{76} + 92 q^{82} - 20 q^{85} + 84 q^{88} + 80 q^{91} + 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.2.f.a 135.f 15.e $8$ $1.078$ 8.0.\(\cdots\).1 None 135.2.f.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
135.2.f.b 135.f 15.e $8$ $1.078$ 8.0.\(\cdots\).8 None 135.2.f.b \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3}+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

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