Properties

Label 135.4.b
Level $135$
Weight $4$
Character orbit 135.b
Rep. character $\chi_{135}(109,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(135, [\chi])\).

Total New Old
Modular forms 60 24 36
Cusp forms 48 24 24
Eisenstein series 12 0 12

Trace form

\( 24 q - 102 q^{4} + O(q^{10}) \) \( 24 q - 102 q^{4} + 72 q^{10} + 438 q^{16} - 108 q^{19} - 354 q^{25} + 180 q^{31} + 1830 q^{34} - 582 q^{40} - 258 q^{46} - 2460 q^{49} + 1458 q^{55} - 2088 q^{61} - 2700 q^{64} - 4158 q^{70} + 7914 q^{76} + 1440 q^{79} - 432 q^{85} - 4104 q^{91} - 2556 q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.4.b.a 135.b 5.b $4$ $7.965$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-13-\beta _{3})q^{4}-5\beta _{1}q^{5}+\cdots\)
135.4.b.b 135.b 5.b $8$ $7.965$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{5}+\cdots\)
135.4.b.c 135.b 5.b $12$ $7.965$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(-5-\beta _{1})q^{4}-\beta _{3}q^{5}+\beta _{8}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)