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Properties

Label 138.5.b
Level $138$
Weight $5$
Character orbit 138.b
Rep. character $\chi_{138}(91,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 138.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(138, [\chi])\).

Total New Old
Modular forms 100 16 84
Cusp forms 92 16 76
Eisenstein series 8 0 8

Trace form

\( 16 q + 128 q^{4} + 432 q^{9} + O(q^{10}) \) \( 16 q + 128 q^{4} + 432 q^{9} - 208 q^{13} + 1024 q^{16} + 840 q^{23} + 1056 q^{25} + 1920 q^{26} + 3600 q^{29} + 224 q^{31} - 3264 q^{35} + 3456 q^{36} - 2016 q^{39} - 6144 q^{41} + 1280 q^{46} + 8880 q^{47} - 13888 q^{49} + 7296 q^{50} - 1664 q^{52} + 832 q^{55} + 2944 q^{58} - 18240 q^{59} + 8192 q^{64} + 10584 q^{69} + 19584 q^{70} - 30048 q^{71} + 9536 q^{73} - 4176 q^{75} + 14160 q^{77} + 6912 q^{78} + 11664 q^{81} - 19584 q^{82} - 32496 q^{85} - 8064 q^{87} + 6720 q^{92} - 11952 q^{93} - 21248 q^{94} - 20064 q^{95} + 21504 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.5.b.a 138.b 23.b $16$ $14.265$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+8q^{4}+\beta _{4}q^{5}+\beta _{7}q^{6}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)