Properties

Label 210.3.s
Level 210
Weight 3
Character orbit s
Rep. character \(\chi_{210}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 40
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 40 168
Cusp forms 176 40 136
Eisenstein series 32 0 32

Trace form

\( 40q + 40q^{4} - 8q^{6} + 20q^{7} - 4q^{9} + O(q^{10}) \) \( 40q + 40q^{4} - 8q^{6} + 20q^{7} - 4q^{9} + 136q^{13} + 40q^{15} - 80q^{16} + 16q^{18} - 140q^{19} + 36q^{21} - 8q^{24} + 100q^{25} - 120q^{27} - 16q^{28} - 20q^{30} + 4q^{31} + 232q^{33} + 32q^{34} - 16q^{36} - 76q^{37} - 4q^{39} + 128q^{42} - 104q^{43} - 20q^{45} - 56q^{46} + 100q^{49} + 168q^{51} + 136q^{52} + 40q^{54} + 80q^{55} + 200q^{57} + 144q^{58} + 40q^{60} - 120q^{61} - 324q^{63} - 320q^{64} - 288q^{66} - 20q^{67} - 416q^{69} - 120q^{70} - 32q^{72} - 476q^{73} - 560q^{76} - 192q^{78} - 508q^{79} - 304q^{81} + 224q^{82} + 144q^{84} - 240q^{85} - 324q^{87} + 468q^{91} + 204q^{93} + 400q^{94} + 16q^{96} - 512q^{97} + 208q^{99} + O(q^{100}) \)

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.s.a \(40\) \(5.722\) None \(0\) \(0\) \(0\) \(20\)

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

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database