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Properties

Label 429.2.p
Level $429$
Weight $2$
Character orbit 429.p
Rep. character $\chi_{429}(230,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

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

\( 104q - 2q^{3} - 52q^{4} + 2q^{9} + O(q^{10}) \) \( 104q - 2q^{3} - 52q^{4} + 2q^{9} + 12q^{12} + 8q^{15} - 60q^{16} + 16q^{22} - 80q^{25} + 4q^{27} - 32q^{31} - 4q^{33} - 56q^{34} + 32q^{36} - 4q^{37} - 22q^{42} + 22q^{45} + 8q^{48} + 16q^{49} + 12q^{55} - 16q^{58} - 12q^{60} + 40q^{64} + 68q^{66} + 28q^{67} + 38q^{69} + 88q^{70} - 54q^{75} - 28q^{78} - 38q^{81} + 32q^{82} - 8q^{88} - 28q^{91} + 26q^{93} - 36q^{97} - 116q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a \(8\) \(3.426\) 8.0.\(\cdots\).7 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}-2\beta _{6}q^{5}+\cdots\)
429.2.p.b \(96\) \(3.426\) None \(0\) \(2\) \(0\) \(0\)