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Properties

Label 105.3.v
Level $105$
Weight $3$
Character orbit 105.v
Rep. character $\chi_{105}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

Total New Old
Modular forms 144 64 80
Cusp forms 112 64 48
Eisenstein series 32 0 32

Trace form

\( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8} - 16 q^{10} + 16 q^{11} - 48 q^{15} + 80 q^{16} + 56 q^{17} + 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 288 q^{26} - 380 q^{28} - 48 q^{30} - 136 q^{31} - 48 q^{32}+ \cdots + 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.3.v.a 105.v 35.l $64$ $2.861$ None 105.3.v.a \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)