Properties

Label 105.4.u
Level $105$
Weight $4$
Character orbit 105.u
Rep. character $\chi_{105}(52,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $96$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 208 96 112
Cusp forms 176 96 80
Eisenstein series 32 0 32

Trace form

\( 96 q + 48 q^{5} - 4 q^{7} + 168 q^{8} - 72 q^{10} + 56 q^{11} - 168 q^{15} + 880 q^{16} + 96 q^{21} + 624 q^{22} - 64 q^{23} + 152 q^{25} + 912 q^{26} + 628 q^{28} + 48 q^{30} - 528 q^{31} - 672 q^{32}+ \cdots + 20184 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.4.u.a 105.u 35.k $96$ $6.195$ None 105.4.u.a \(0\) \(0\) \(48\) \(-4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)