Properties

Label 429.2.n
Level $429$
Weight $2$
Character orbit 429.n
Rep. character $\chi_{429}(157,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $4$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
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 96 144
Cusp forms 208 96 112
Eisenstein series 32 0 32

Trace form

\( 96q + 8q^{2} - 16q^{4} + 8q^{5} + 4q^{6} + 4q^{7} - 16q^{8} - 24q^{9} + O(q^{10}) \) \( 96q + 8q^{2} - 16q^{4} + 8q^{5} + 4q^{6} + 4q^{7} - 16q^{8} - 24q^{9} + 16q^{10} + 12q^{11} + 8q^{12} + 4q^{13} - 4q^{14} - 12q^{15} - 52q^{16} - 24q^{17} - 12q^{18} + 16q^{19} + 32q^{20} - 32q^{21} + 28q^{22} + 48q^{23} + 12q^{24} - 16q^{25} + 20q^{29} + 4q^{30} - 24q^{31} + 16q^{32} + 16q^{33} - 32q^{34} - 40q^{35} - 16q^{36} - 36q^{37} + 64q^{38} + 8q^{39} - 96q^{40} - 4q^{42} + 48q^{43} - 128q^{44} + 8q^{45} - 44q^{46} + 48q^{47} - 24q^{48} + 20q^{49} - 76q^{50} - 4q^{51} - 16q^{53} - 16q^{54} - 56q^{55} + 96q^{56} + 64q^{58} + 8q^{59} + 24q^{60} - 60q^{62} + 4q^{63} - 96q^{64} + 36q^{66} + 60q^{68} + 16q^{69} + 28q^{70} + 8q^{71} + 4q^{72} - 28q^{73} + 104q^{74} - 8q^{75} - 112q^{76} - 16q^{77} - 44q^{79} - 156q^{80} - 24q^{81} + 84q^{82} + 56q^{83} + 44q^{85} + 32q^{86} + 16q^{87} + 60q^{88} + 56q^{89} - 4q^{90} + 8q^{91} - 16q^{92} - 56q^{93} - 80q^{94} - 60q^{95} + 28q^{96} + 104q^{97} - 256q^{98} - 28q^{99} + O(q^{100}) \)

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.n.a \(12\) \(3.426\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-3\) \(8\) \(5\) \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
429.2.n.b \(20\) \(3.426\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1\) \(5\) \(4\) \(-3\) \(q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
429.2.n.c \(28\) \(3.426\) None \(1\) \(7\) \(-4\) \(1\)
429.2.n.d \(36\) \(3.426\) None \(3\) \(-9\) \(0\) \(1\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)