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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.q.a \(16\) \(0.838\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots\)

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

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