Properties

Label 430.2.k
Level $430$
Weight $2$
Character orbit 430.k
Rep. character $\chi_{430}(11,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $72$
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.k (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{7})\)
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 420 72 348
Cusp forms 372 72 300
Eisenstein series 48 0 48

Trace form

\( 72 q + 2 q^{2} + 8 q^{3} - 12 q^{4} + 2 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} - 10 q^{9} + O(q^{10}) \) \( 72 q + 2 q^{2} + 8 q^{3} - 12 q^{4} + 2 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} - 10 q^{9} + 8 q^{11} + 8 q^{12} + 20 q^{13} - 10 q^{14} - 12 q^{16} + 8 q^{17} + 10 q^{18} - 14 q^{19} + 2 q^{20} + 16 q^{21} - 26 q^{22} - 16 q^{23} - 6 q^{24} - 12 q^{25} - 20 q^{26} + 32 q^{27} + 16 q^{28} + 12 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} + 8 q^{35} + 32 q^{36} - 72 q^{37} - 8 q^{38} - 36 q^{39} + 24 q^{41} - 32 q^{42} - 14 q^{43} - 20 q^{44} - 30 q^{45} - 12 q^{46} - 8 q^{47} + 8 q^{48} + 28 q^{49} - 12 q^{50} - 70 q^{51} - 36 q^{52} + 20 q^{53} - 10 q^{54} + 8 q^{55} + 4 q^{56} - 12 q^{57} + 40 q^{58} - 60 q^{59} + 56 q^{61} + 24 q^{62} - 12 q^{63} - 12 q^{64} + 16 q^{65} + 8 q^{66} + 32 q^{67} + 8 q^{68} + 26 q^{69} + 16 q^{70} + 16 q^{71} + 10 q^{72} + 56 q^{73} + 12 q^{74} - 6 q^{75} + 28 q^{76} + 72 q^{77} + 24 q^{78} - 24 q^{79} - 12 q^{80} - 20 q^{81} + 52 q^{82} - 6 q^{83} + 16 q^{84} - 16 q^{85} - 68 q^{86} - 120 q^{87} - 26 q^{88} + 32 q^{89} + 16 q^{90} + 8 q^{91} - 16 q^{92} - 112 q^{93} - 12 q^{94} - 4 q^{95} + 8 q^{96} + 44 q^{97} + 26 q^{98} + 58 q^{99} + O(q^{100}) \)

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.k.a 430.k 43.e $12$ $3.434$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-1\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\beta _{7}+\beta _{8}-\beta _{9}+\beta _{10}-\beta _{11})q^{2}+\cdots\)
430.2.k.b 430.k 43.e $18$ $3.434$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(2\) \(3\) \(6\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}-\beta _{10}q^{5}+\cdots\)
430.2.k.c 430.k 43.e $18$ $3.434$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(3\) \(5\) \(-3\) \(8\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{12}q^{2}+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{7}+\cdots)q^{4}+\cdots\)
430.2.k.d 430.k 43.e $24$ $3.434$ None \(4\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{7}]$

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

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