Properties

Label 138.4.f
Level $138$
Weight $4$
Character orbit 138.f
Rep. character $\chi_{138}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $240$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 138.f (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(138, [\chi])\).

Total New Old
Modular forms 760 240 520
Cusp forms 680 240 440
Eisenstein series 80 0 80

Trace form

\( 240 q - 8 q^{3} + 96 q^{4} - 8 q^{6} - 36 q^{9} + 32 q^{12} - 96 q^{13} - 748 q^{15} - 384 q^{16} - 40 q^{18} + 1320 q^{21} + 32 q^{24} - 144 q^{25} - 56 q^{27} - 1496 q^{30} - 72 q^{31} - 1936 q^{33} + 144 q^{36}+ \cdots + 2310 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.4.f.a 138.f 69.g $240$ $8.142$ None 138.4.f.a \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{4}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(138, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)