Properties

Label 210.3.v
Level 210
Weight 3
Character orbit v
Rep. character \(\chi_{210}(37,\cdot)\)
Character field \(\Q(\zeta_{12})\)
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.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

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

Trace form

\( 64q - 8q^{5} + 16q^{7} + O(q^{10}) \) \( 64q - 8q^{5} + 16q^{7} + 16q^{10} - 16q^{11} + 48q^{15} + 128q^{16} - 112q^{17} - 48q^{21} + 96q^{22} - 48q^{23} + 40q^{25} + 64q^{26} + 112q^{28} + 48q^{30} + 272q^{31} + 24q^{33} + 40q^{35} + 384q^{36} - 8q^{37} - 64q^{38} - 416q^{41} - 48q^{42} - 496q^{43} - 96q^{46} - 440q^{47} + 48q^{51} - 48q^{53} - 208q^{55} + 128q^{56} + 192q^{57} - 208q^{58} + 432q^{61} - 96q^{62} + 120q^{63} - 136q^{65} + 128q^{67} + 224q^{68} - 288q^{70} - 480q^{71} + 136q^{73} - 96q^{75} + 256q^{76} - 1160q^{77} - 192q^{78} + 32q^{80} + 288q^{81} - 128q^{82} - 1152q^{83} + 464q^{85} - 128q^{86} - 144q^{87} + 96q^{88} + 720q^{91} + 192q^{92} - 48q^{93} + 440q^{95} + 80q^{97} - 128q^{98} + O(q^{100}) \)

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.v.a \(32\) \(5.722\) None \(-16\) \(0\) \(0\) \(-8\)
210.3.v.b \(32\) \(5.722\) None \(16\) \(0\) \(-8\) \(24\)

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