Properties

Label 210.3.w
Level 210
Weight 3
Character orbit w
Rep. character \(\chi_{210}(17,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 128
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.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 416 128 288
Cusp forms 352 128 224
Eisenstein series 64 0 64

Trace form

\( 128q + 8q^{7} + O(q^{10}) \) \( 128q + 8q^{7} + 48q^{10} + 24q^{15} + 256q^{16} - 32q^{18} + 72q^{21} + 32q^{22} - 32q^{25} + 16q^{28} + 48q^{30} + 60q^{33} + 32q^{36} - 64q^{37} - 224q^{42} + 64q^{43} - 588q^{45} - 48q^{46} - 168q^{51} - 536q^{57} + 112q^{58} + 32q^{60} + 1200q^{61} - 324q^{63} + 32q^{67} + 64q^{72} - 1248q^{73} - 96q^{75} - 256q^{78} - 128q^{81} - 384q^{82} - 304q^{85} - 612q^{87} - 32q^{88} - 464q^{91} - 372q^{93} - 96q^{96} + O(q^{100}) \)

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.w.a \(64\) \(5.722\) None \(-32\) \(-6\) \(-12\) \(4\)
210.3.w.b \(64\) \(5.722\) None \(32\) \(6\) \(12\) \(4\)

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