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Properties

Label 430.2.q
Level $430$
Weight $2$
Character orbit 430.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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
430.2.q.a 430.q 43.g $36$ $3.434$ None \(-6\) \(5\) \(3\) \(1\) $\mathrm{SU}(2)[C_{21}]$
430.2.q.b 430.q 43.g $48$ $3.434$ None \(-8\) \(-1\) \(-4\) \(-7\) $\mathrm{SU}(2)[C_{21}]$
430.2.q.c 430.q 43.g $48$ $3.434$ None \(8\) \(-7\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{21}]$
430.2.q.d 430.q 43.g $60$ $3.434$ None \(10\) \(-1\) \(-5\) \(1\) $\mathrm{SU}(2)[C_{21}]$

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

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