Properties

Label 429.2.j
Level $429$
Weight $2$
Character orbit 429.j
Rep. character $\chi_{429}(122,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 120 96 24
Cusp forms 104 96 8
Eisenstein series 16 0 16

Trace form

\( 96q + 12q^{6} - 16q^{7} + O(q^{10}) \) \( 96q + 12q^{6} - 16q^{7} + 16q^{13} - 16q^{15} - 120q^{16} - 28q^{18} - 24q^{19} + 24q^{24} - 24q^{27} + 56q^{28} + 48q^{31} - 16q^{34} - 16q^{37} + 80q^{40} + 52q^{42} + 4q^{45} - 56q^{46} + 28q^{48} + 4q^{54} + 4q^{57} + 48q^{58} + 4q^{60} - 96q^{61} - 36q^{63} + 20q^{66} - 16q^{67} + 48q^{70} - 16q^{72} - 16q^{73} - 88q^{76} + 80q^{78} + 16q^{79} + 32q^{81} + 52q^{84} - 8q^{85} - 48q^{87} - 16q^{91} - 36q^{93} - 16q^{94} - 108q^{96} - 48q^{97} + O(q^{100}) \)

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.j.a \(96\) \(3.426\) None \(0\) \(0\) \(0\) \(-16\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)