Properties

Label 429.2.y
Level $429$
Weight $2$
Character orbit 429.y
Rep. character $\chi_{429}(116,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $208$
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.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{10})\)
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 240 240 0
Cusp forms 208 208 0
Eisenstein series 32 32 0

Trace form

\( 208q - 6q^{3} + 36q^{4} - 18q^{9} + O(q^{10}) \) \( 208q - 6q^{3} + 36q^{4} - 18q^{9} - 12q^{12} - 10q^{13} - 56q^{16} - 68q^{22} - 60q^{25} + 6q^{27} + 80q^{30} - 68q^{36} + 50q^{39} + 60q^{40} + 52q^{42} - 40q^{48} - 32q^{49} - 90q^{51} - 50q^{52} + 12q^{55} + 92q^{64} - 122q^{66} + 96q^{69} + 22q^{75} - 112q^{78} - 60q^{79} - 2q^{81} + 60q^{82} - 188q^{88} + 160q^{90} + 62q^{91} - 180q^{94} + O(q^{100}) \)

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.y.a \(32\) \(3.426\) \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\)
429.2.y.b \(176\) \(3.426\) None \(0\) \(-6\) \(0\) \(0\)