Properties

Label 430.2.q
Level 430
Weight 2
Character orbit q
Rep. character \(\chi_{430}(31,\cdot)\)
Character field \(\Q(\zeta_{21})\)
Dimension 192
Newform subspaces 4
Sturm bound 132
Trace bound 2

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Defining parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 430.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 43 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 4 \)
Sturm bound: \(132\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(430, [\chi])\).

Total New Old
Modular forms 840 192 648
Cusp forms 744 192 552
Eisenstein series 96 0 96

Trace form

\( 192q + 4q^{2} - 4q^{3} - 32q^{4} - 2q^{5} - 2q^{6} - 8q^{7} + 4q^{8} + 32q^{9} + O(q^{10}) \) \( 192q + 4q^{2} - 4q^{3} - 32q^{4} - 2q^{5} - 2q^{6} - 8q^{7} + 4q^{8} + 32q^{9} + 4q^{11} - 4q^{12} + 10q^{14} - 32q^{16} - 2q^{17} - 10q^{18} + 52q^{19} - 2q^{20} - 8q^{21} + 38q^{22} + 16q^{23} + 12q^{24} + 16q^{25} + 20q^{26} + 32q^{27} - 8q^{28} + 6q^{29} - 2q^{30} + 36q^{31} + 4q^{32} + 18q^{33} - 66q^{34} - 8q^{35} - 122q^{36} - 40q^{37} + 38q^{38} - 104q^{39} - 24q^{41} - 112q^{42} + 54q^{43} - 52q^{44} + 48q^{45} - 108q^{46} - 40q^{47} - 4q^{48} - 152q^{49} + 12q^{50} - 2q^{51} - 56q^{52} + 4q^{53} - 56q^{54} - 8q^{55} - 4q^{56} + 88q^{57} - 28q^{58} + 96q^{59} + 36q^{61} - 12q^{62} + 104q^{63} - 32q^{64} + 8q^{65} + 52q^{66} + 42q^{67} - 2q^{68} - 8q^{69} + 32q^{70} - 16q^{71} - 10q^{72} - 102q^{73} + 48q^{74} - 20q^{75} + 10q^{76} + 12q^{77} + 72q^{78} + 20q^{79} + 12q^{80} - 144q^{81} + 20q^{82} - 78q^{83} - 8q^{84} - 56q^{85} + 128q^{86} + 168q^{87} + 38q^{88} - 8q^{89} - 16q^{90} - 52q^{91} + 16q^{92} - 12q^{93} + 36q^{94} - 44q^{95} - 2q^{96} + 72q^{97} + 46q^{98} + 38q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(430, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
430.2.q.a \(36\) \(3.434\) None \(-6\) \(5\) \(3\) \(1\)
430.2.q.b \(48\) \(3.434\) None \(-8\) \(-1\) \(-4\) \(-7\)
430.2.q.c \(48\) \(3.434\) None \(8\) \(-7\) \(4\) \(-3\)
430.2.q.d \(60\) \(3.434\) None \(10\) \(-1\) \(-5\) \(1\)

Decomposition of \(S_{2}^{\mathrm{old}}(430, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(430, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database