Properties

Label 210.3.q
Level 210
Weight 3
Character orbit q
Rep. character \(\chi_{210}(149,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newform subspaces 1
Sturm bound 144
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(210, [\chi])\).

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64q - 64q^{4} + 8q^{6} - 4q^{9} + O(q^{10}) \) \( 64q - 64q^{4} + 8q^{6} - 4q^{9} - 8q^{10} + 4q^{15} - 128q^{16} + 8q^{19} - 88q^{21} - 8q^{24} + 12q^{25} - 8q^{30} + 152q^{31} + 16q^{36} - 208q^{39} - 16q^{40} + 106q^{45} - 56q^{46} - 64q^{49} - 140q^{51} - 56q^{54} + 616q^{55} - 4q^{60} + 104q^{61} + 512q^{64} - 160q^{66} + 456q^{69} - 144q^{70} + 298q^{75} - 32q^{76} - 360q^{79} + 304q^{81} - 80q^{84} - 408q^{85} - 688q^{90} - 288q^{91} + 240q^{94} - 16q^{96} - 568q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
210.3.q.a \(64\) \(5.722\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database