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Properties

Label 115.3.h
Level $115$
Weight $3$
Character orbit 115.h
Rep. character $\chi_{115}(11,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $160$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.h (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(115, [\chi])\).

Total New Old
Modular forms 260 160 100
Cusp forms 220 160 60
Eisenstein series 40 0 40

Trace form

\( 160 q + 4 q^{2} - 16 q^{4} - 26 q^{6} - 22 q^{8} - 32 q^{9} + 30 q^{12} + 12 q^{13} - 256 q^{16} - 110 q^{17} + 70 q^{18} - 66 q^{19} - 66 q^{21} - 34 q^{23} + 180 q^{24} + 80 q^{25} + 238 q^{26} + 234 q^{27}+ \cdots + 2112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.3.h.a 115.h 23.d $160$ $3.134$ None 115.3.h.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{3}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(115, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)