Properties

Label 429.2.bs
Level $429$
Weight $2$
Character orbit 429.bs
Rep. character $\chi_{429}(7,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $448$
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{60})\)
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 960 448 512
Cusp forms 832 448 384
Eisenstein series 128 0 128

Trace form

\( 448q + 56q^{9} + O(q^{10}) \) \( 448q + 56q^{9} - 24q^{11} - 20q^{13} + 16q^{15} - 32q^{16} + 28q^{20} + 20q^{22} - 96q^{23} - 60q^{24} + 8q^{26} + 40q^{29} + 8q^{31} - 4q^{33} - 176q^{34} - 24q^{37} + 120q^{41} + 24q^{42} - 48q^{44} - 80q^{46} - 52q^{47} + 16q^{48} - 100q^{52} + 24q^{53} + 20q^{55} - 144q^{56} - 112q^{58} - 184q^{59} + 72q^{60} + 40q^{61} - 80q^{66} - 168q^{67} - 120q^{68} - 64q^{70} + 32q^{71} - 60q^{73} + 136q^{78} + 80q^{79} + 144q^{80} + 56q^{81} - 132q^{82} - 320q^{83} + 80q^{85} - 32q^{86} - 12q^{88} + 192q^{89} + 64q^{92} + 32q^{93} - 80q^{94} - 600q^{95} - 100q^{96} - 28q^{97} + 4q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
429.2.bs.a \(224\) \(3.426\) None \(0\) \(-28\) \(-6\) \(0\)
429.2.bs.b \(224\) \(3.426\) None \(0\) \(28\) \(6\) \(0\)

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

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