Properties

Label 429.2.t
Level $429$
Weight $2$
Character orbit 429.t
Rep. character $\chi_{429}(296,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{6})\)
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 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104q - 2q^{3} + 44q^{4} - 6q^{9} + O(q^{10}) \) \( 104q - 2q^{3} + 44q^{4} - 6q^{9} - 4q^{12} - 36q^{15} - 44q^{16} - 12q^{22} + 64q^{25} + 4q^{27} + 12q^{33} + 28q^{36} - 12q^{37} + 50q^{42} - 66q^{45} + 16q^{48} - 24q^{49} - 8q^{55} - 24q^{58} - 104q^{64} - 60q^{66} - 60q^{67} - 42q^{69} - 42q^{75} + 16q^{78} - 22q^{81} - 16q^{82} + 92q^{88} - 84q^{91} + 126q^{93} + 36q^{97} + O(q^{100}) \)

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.t.a \(104\) \(3.426\) None \(0\) \(-2\) \(0\) \(0\)