Properties

Label 429.2.bn
Level $429$
Weight $2$
Character orbit 429.bn
Rep. character $\chi_{429}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $224$
Newform subspaces $2$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 480 224 256
Cusp forms 416 224 192
Eisenstein series 64 0 64

Trace form

\( 224 q - 28 q^{4} + 28 q^{9} + O(q^{10}) \) \( 224 q - 28 q^{4} + 28 q^{9} - 40 q^{10} + 36 q^{11} + 16 q^{12} - 14 q^{13} + 24 q^{14} - 12 q^{15} + 24 q^{16} + 8 q^{17} - 24 q^{19} - 24 q^{20} - 26 q^{22} + 20 q^{23} + 44 q^{25} - 48 q^{26} + 36 q^{28} - 12 q^{29} + 20 q^{30} + 6 q^{33} + 4 q^{35} - 28 q^{36} + 68 q^{38} - 8 q^{39} - 40 q^{40} + 36 q^{41} - 12 q^{42} - 96 q^{43} + 36 q^{46} - 40 q^{48} - 80 q^{49} + 60 q^{50} - 56 q^{51} - 2 q^{52} - 68 q^{53} - 16 q^{55} - 176 q^{56} + 120 q^{58} + 54 q^{59} - 12 q^{61} + 8 q^{62} - 32 q^{64} + 52 q^{65} - 56 q^{66} - 20 q^{68} - 14 q^{69} + 48 q^{71} + 52 q^{74} + 32 q^{75} - 264 q^{76} - 132 q^{77} - 40 q^{78} + 72 q^{79} - 48 q^{80} + 28 q^{81} + 34 q^{82} - 60 q^{85} + 112 q^{87} + 80 q^{88} - 216 q^{89} - 40 q^{90} - 78 q^{91} + 68 q^{92} - 24 q^{93} - 28 q^{94} + 132 q^{95} - 162 q^{97} + 96 q^{98} + O(q^{100}) \)

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.bn.a 429.bn 143.u $112$ $3.426$ None \(0\) \(-14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$
429.2.bn.b 429.bn 143.u $112$ $3.426$ None \(0\) \(14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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