Properties

Label 429.2.bj
Level $429$
Weight $2$
Character orbit 429.bj
Rep. character $\chi_{429}(73,\cdot)$
Character field $\Q(\zeta_{20})$
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.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 224q - 56q^{9} + O(q^{10}) \) \( 224q - 56q^{9} - 24q^{11} + 20q^{13} - 48q^{14} + 8q^{15} + 32q^{16} - 76q^{20} + 40q^{22} + 60q^{24} - 8q^{26} - 40q^{29} - 32q^{31} + 4q^{33} - 64q^{34} + 24q^{37} - 120q^{41} + 48q^{42} - 12q^{44} - 40q^{46} - 92q^{47} - 112q^{48} + 100q^{52} + 120q^{53} - 32q^{55} - 32q^{58} - 20q^{59} - 72q^{60} - 40q^{61} + 56q^{66} + 72q^{67} + 120q^{68} - 80q^{70} - 32q^{71} + 60q^{73} - 136q^{78} - 80q^{79} - 48q^{80} - 56q^{81} + 140q^{83} - 80q^{85} + 80q^{86} - 48q^{89} - 48q^{91} - 64q^{92} + 16q^{93} - 40q^{94} + 100q^{96} + 100q^{97} - 4q^{99} + O(q^{100}) \)

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.bj.a \(112\) \(3.426\) None \(0\) \(-28\) \(-6\) \(0\)
429.2.bj.b \(112\) \(3.426\) None \(0\) \(28\) \(6\) \(0\)

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

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