Properties

Label 210.3.c
Level 210
Weight 3
Character orbit c
Rep. character \(\chi_{210}(29,\cdot)\)
Character field \(\Q\)
Dimension 24
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
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 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24q + 48q^{4} + 44q^{9} + O(q^{10}) \) \( 24q + 48q^{4} + 44q^{9} + 16q^{10} + 4q^{15} + 96q^{16} - 80q^{19} - 28q^{21} + 48q^{25} - 56q^{30} + 224q^{31} + 128q^{34} + 88q^{36} - 92q^{39} + 32q^{40} - 72q^{45} - 144q^{46} - 168q^{49} - 284q^{51} - 144q^{54} - 320q^{55} + 8q^{60} + 192q^{64} + 224q^{66} - 152q^{69} - 56q^{70} + 48q^{75} - 160q^{76} - 72q^{79} - 212q^{81} - 56q^{84} - 64q^{85} - 240q^{90} + 168q^{91} - 128q^{94} - 876q^{99} + O(q^{100}) \)

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.c.a \(24\) \(5.722\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database