Properties

Label 105.2.q
Level $105$
Weight $2$
Character orbit 105.q
Rep. character $\chi_{105}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 24 16 8
Eisenstein series 16 0 16

Trace form

\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} + 16 q^{36} - 4 q^{39} + 32 q^{40} + 16 q^{41} + 20 q^{44} - 2 q^{45} - 32 q^{46} - 40 q^{49} - 40 q^{50} + 4 q^{51} - 4 q^{54} + 8 q^{55} + 84 q^{56} + 4 q^{59} + 16 q^{60} + 16 q^{61} + 16 q^{64} + 30 q^{65} + 28 q^{66} + 40 q^{69} + 16 q^{70} - 56 q^{71} + 40 q^{74} + 8 q^{75} - 64 q^{76} - 16 q^{79} + 52 q^{80} - 8 q^{81} + 12 q^{84} - 64 q^{85} - 48 q^{86} + 16 q^{89} - 8 q^{90} + 8 q^{91} - 32 q^{94} - 22 q^{95} + 8 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.q.a 105.q 35.j $16$ $0.838$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

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