Properties

Label 429.2.i
Level $429$
Weight $2$
Character orbit 429.i
Rep. character $\chi_{429}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $6$
Sturm bound $112$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(429, [\chi])\).

Total New Old
Modular forms 120 44 76
Cusp forms 104 44 60
Eisenstein series 16 0 16

Trace form

\( 44q + 4q^{2} + 2q^{3} - 20q^{4} + 16q^{5} - 2q^{7} - 24q^{8} - 22q^{9} + O(q^{10}) \) \( 44q + 4q^{2} + 2q^{3} - 20q^{4} + 16q^{5} - 2q^{7} - 24q^{8} - 22q^{9} - 4q^{10} - 8q^{12} + 14q^{13} + 16q^{14} - 24q^{16} - 16q^{17} - 8q^{18} - 28q^{20} + 20q^{21} + 4q^{22} + 4q^{23} + 52q^{25} - 16q^{26} - 4q^{27} - 24q^{28} - 8q^{29} - 28q^{31} + 68q^{32} - 8q^{34} + 8q^{35} - 20q^{36} + 48q^{38} + 4q^{39} + 64q^{40} - 24q^{41} - 12q^{42} - 6q^{43} + 16q^{44} - 8q^{45} - 48q^{46} + 8q^{47} + 8q^{48} - 28q^{49} - 36q^{50} + 16q^{51} + 28q^{52} + 32q^{53} + 16q^{55} - 56q^{56} - 48q^{57} - 20q^{58} - 56q^{60} - 22q^{61} - 12q^{62} - 2q^{63} + 24q^{64} - 48q^{65} - 16q^{66} + 14q^{67} + 28q^{68} + 16q^{69} + 128q^{70} + 20q^{71} + 12q^{72} + 28q^{73} - 36q^{74} + 6q^{75} + 56q^{76} + 12q^{78} + 4q^{79} - 20q^{80} - 22q^{81} + 56q^{82} + 32q^{83} - 28q^{84} + 48q^{85} - 24q^{86} - 4q^{87} + 44q^{89} + 8q^{90} - 62q^{91} - 160q^{92} + 2q^{93} - 76q^{94} + 24q^{95} + 40q^{96} - 6q^{97} - 36q^{98} + O(q^{100}) \)

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.i.a \(2\) \(3.426\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(-1\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+2q^{5}-\zeta_{6}q^{7}+\cdots\)
429.2.i.b \(2\) \(3.426\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(3\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+2q^{5}+3\zeta_{6}q^{7}+\cdots\)
429.2.i.c \(10\) \(3.426\) 10.0.\(\cdots\).1 None \(-2\) \(-5\) \(16\) \(-9\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{6})q^{4}+\cdots\)
429.2.i.d \(10\) \(3.426\) 10.0.\(\cdots\).1 None \(0\) \(5\) \(-4\) \(-7\) \(q+(\beta _{2}+\beta _{7}-\beta _{8}+\beta _{9})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
429.2.i.e \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(5\) \(4\) \(9\) \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
429.2.i.f \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(-5\) \(-8\) \(3\) \(q+(1-\beta _{1}-\beta _{6})q^{2}+(-1+\beta _{6})q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(429, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)