Properties

Label 429.2.n
Level $429$
Weight $2$
Character orbit 429.n
Rep. character $\chi_{429}(157,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $4$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).

Total New Old
Modular forms 240 96 144
Cusp forms 208 96 112
Eisenstein series 32 0 32

Trace form

\( 96 q + 8 q^{2} - 16 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{7} - 16 q^{8} - 24 q^{9} + O(q^{10}) \) \( 96 q + 8 q^{2} - 16 q^{4} + 8 q^{5} + 4 q^{6} + 4 q^{7} - 16 q^{8} - 24 q^{9} + 16 q^{10} + 12 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{15} - 52 q^{16} - 24 q^{17} - 12 q^{18} + 16 q^{19} + 32 q^{20} - 32 q^{21} + 28 q^{22} + 48 q^{23} + 12 q^{24} - 16 q^{25} + 20 q^{29} + 4 q^{30} - 24 q^{31} + 16 q^{32} + 16 q^{33} - 32 q^{34} - 40 q^{35} - 16 q^{36} - 36 q^{37} + 64 q^{38} + 8 q^{39} - 96 q^{40} - 4 q^{42} + 48 q^{43} - 128 q^{44} + 8 q^{45} - 44 q^{46} + 48 q^{47} - 24 q^{48} + 20 q^{49} - 76 q^{50} - 4 q^{51} - 16 q^{53} - 16 q^{54} - 56 q^{55} + 96 q^{56} + 64 q^{58} + 8 q^{59} + 24 q^{60} - 60 q^{62} + 4 q^{63} - 96 q^{64} + 36 q^{66} + 60 q^{68} + 16 q^{69} + 28 q^{70} + 8 q^{71} + 4 q^{72} - 28 q^{73} + 104 q^{74} - 8 q^{75} - 112 q^{76} - 16 q^{77} - 44 q^{79} - 156 q^{80} - 24 q^{81} + 84 q^{82} + 56 q^{83} + 44 q^{85} + 32 q^{86} + 16 q^{87} + 60 q^{88} + 56 q^{89} - 4 q^{90} + 8 q^{91} - 16 q^{92} - 56 q^{93} - 80 q^{94} - 60 q^{95} + 28 q^{96} + 104 q^{97} - 256 q^{98} - 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
429.2.n.a 429.n 11.c $12$ $3.426$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-3\) \(8\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
429.2.n.b 429.n 11.c $20$ $3.426$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1\) \(5\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
429.2.n.c 429.n 11.c $28$ $3.426$ None \(1\) \(7\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{5}]$
429.2.n.d 429.n 11.c $36$ $3.426$ None \(3\) \(-9\) \(0\) \(1\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(429, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)