Properties

Label 429.2.x
Level $429$
Weight $2$
Character orbit 429.x
Rep. character $\chi_{429}(248,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 240 192 48
Cusp forms 208 192 16
Eisenstein series 32 0 32

Trace form

\( 192q + 6q^{3} - 48q^{4} - 10q^{6} - 14q^{9} + O(q^{10}) \) \( 192q + 6q^{3} - 48q^{4} - 10q^{6} - 14q^{9} - 20q^{12} + 6q^{15} - 28q^{16} - 10q^{18} - 60q^{19} + 4q^{22} + 30q^{24} - 12q^{25} + 30q^{27} - 20q^{28} + 12q^{31} - 32q^{33} + 56q^{34} + 44q^{36} + 60q^{40} - 108q^{42} - 40q^{45} - 28q^{48} - 24q^{49} + 10q^{51} + 20q^{52} - 20q^{55} + 50q^{57} - 60q^{58} + 36q^{60} + 20q^{61} - 30q^{63} + 64q^{64} - 30q^{66} - 120q^{67} - 16q^{69} + 20q^{70} + 150q^{72} - 20q^{73} + 18q^{75} + 40q^{78} - 160q^{79} - 46q^{81} + 88q^{82} - 40q^{85} + 72q^{88} - 80q^{90} + 8q^{91} - 72q^{93} - 120q^{94} - 140q^{96} - 88q^{97} + 62q^{99} + O(q^{100}) \)

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.x.a \(192\) \(3.426\) None \(0\) \(6\) \(0\) \(0\)

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

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