Properties

Label 105.3.f
Level $105$
Weight $3$
Character orbit 105.f
Rep. character $\chi_{105}(29,\cdot)$
Character field $\Q$
Dimension $24$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
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 36 24 12
Cusp forms 28 24 4
Eisenstein series 8 0 8

Trace form

\( 24q + 52q^{4} - 22q^{9} + O(q^{10}) \) \( 24q + 52q^{4} - 22q^{9} - 24q^{10} + 26q^{15} + 4q^{16} + 72q^{19} + 14q^{21} - 156q^{24} - 64q^{25} - 32q^{30} - 40q^{31} - 144q^{34} + 36q^{36} + 62q^{39} - 40q^{40} + 120q^{45} - 104q^{46} - 168q^{49} + 70q^{51} + 60q^{54} - 16q^{55} - 348q^{60} + 432q^{61} - 364q^{64} + 284q^{66} + 404q^{69} + 140q^{70} + 204q^{75} + 152q^{76} + 108q^{79} - 158q^{81} + 112q^{84} + 196q^{85} - 152q^{90} - 84q^{91} + 808q^{94} - 516q^{96} + 582q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.3.f.a \(24\) \(2.861\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)