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Properties

Label 138.5.h
Level $138$
Weight $5$
Character orbit 138.h
Rep. character $\chi_{138}(7,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $160$
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.h (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{22})\)
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 1000 160 840
Cusp forms 920 160 760
Eisenstein series 80 0 80

Trace form

\( 160 q - 128 q^{4} - 432 q^{9} + O(q^{10}) \) \( 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99} + O(q^{100}) \)

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.h.a 138.h 23.d $160$ $14.265$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

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

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