Properties

Label 210.3.p
Level 210
Weight 3
Character orbit p
Rep. character \(\chi_{210}(19,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 32
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 32 176
Cusp forms 176 32 144
Eisenstein series 32 0 32

Trace form

\( 32q + 32q^{4} + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 32q + 32q^{4} + 12q^{5} - 48q^{9} - 24q^{10} + 48q^{11} - 16q^{14} + 24q^{15} - 64q^{16} + 48q^{19} - 24q^{21} + 72q^{25} + 96q^{26} + 176q^{29} - 24q^{30} - 48q^{31} + 68q^{35} - 192q^{36} - 72q^{39} - 48q^{40} - 96q^{44} - 36q^{45} + 32q^{46} - 272q^{49} + 192q^{50} - 24q^{51} - 64q^{56} + 744q^{59} + 24q^{60} - 672q^{61} - 256q^{64} + 172q^{65} + 320q^{70} - 144q^{71} - 416q^{74} - 144q^{75} + 128q^{79} - 48q^{80} - 144q^{81} - 96q^{84} - 736q^{85} + 304q^{86} - 48q^{89} + 976q^{91} + 528q^{94} + 236q^{95} - 288q^{99} + O(q^{100}) \)

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.p.a \(32\) \(5.722\) None \(0\) \(0\) \(12\) \(0\)

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

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database