Properties

Label 429.2.bb
Level $429$
Weight $2$
Character orbit 429.bb
Rep. character $\chi_{429}(25,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $112$
Newform subspaces $2$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 240 112 128
Cusp forms 208 112 96
Eisenstein series 32 0 32

Trace form

\( 112q + 28q^{4} - 28q^{9} + O(q^{10}) \) \( 112q + 28q^{4} - 28q^{9} + 40q^{10} + 8q^{12} + 2q^{13} - 48q^{14} - 20q^{17} - 76q^{22} + 40q^{23} + 40q^{25} - 18q^{26} + 12q^{29} - 20q^{30} + 8q^{35} + 28q^{36} - 44q^{38} + 8q^{39} + 40q^{40} - 24q^{42} + 48q^{43} - 8q^{48} - 28q^{49} - 28q^{51} + 50q^{52} + 20q^{53} - 56q^{55} - 88q^{56} + 12q^{61} - 140q^{62} - 28q^{64} - 100q^{65} + 44q^{66} + 68q^{68} - 4q^{69} - 76q^{74} - 8q^{75} - 36q^{77} + 40q^{78} + 24q^{79} - 28q^{81} + 32q^{82} - 64q^{87} - 56q^{88} - 20q^{90} - 30q^{91} - 68q^{92} + 52q^{94} + 192q^{95} + O(q^{100}) \)

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.bb.a \(56\) \(3.426\) None \(0\) \(-14\) \(0\) \(0\)
429.2.bb.b \(56\) \(3.426\) None \(0\) \(14\) \(0\) \(0\)

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

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