Properties

Label 210.3.k
Level 210
Weight 3
Character orbit k
Rep. character \(\chi_{210}(83,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 64
Newform subspaces 2
Sturm bound 144
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(23\)

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

\( 64q - 8q^{7} + O(q^{10}) \) \( 64q - 8q^{7} - 24q^{15} - 256q^{16} + 32q^{18} + 24q^{21} - 80q^{22} + 32q^{25} - 16q^{28} + 96q^{30} - 80q^{36} + 64q^{37} - 64q^{42} - 64q^{43} - 96q^{46} + 168q^{51} + 584q^{57} + 224q^{58} - 32q^{60} + 240q^{63} + 64q^{67} - 64q^{72} - 128q^{78} + 152q^{81} - 80q^{85} - 160q^{88} - 544q^{91} - 840q^{93} + O(q^{100}) \)

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.k.a \(32\) \(5.722\) None \(-32\) \(0\) \(0\) \(-4\)
210.3.k.b \(32\) \(5.722\) None \(32\) \(0\) \(0\) \(-4\)

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