Properties

Label 429.2.bd
Level $429$
Weight $2$
Character orbit 429.bd
Rep. character $\chi_{429}(76,\cdot)$
Character field $\Q(\zeta_{12})$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{12})\)
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

\( 112q - 56q^{9} + O(q^{10}) \) \( 112q - 56q^{9} - 16q^{11} - 16q^{15} + 72q^{16} + 72q^{20} - 20q^{22} - 24q^{23} - 8q^{26} - 8q^{31} + 4q^{33} + 16q^{34} + 24q^{37} - 24q^{42} + 48q^{44} - 48q^{47} + 64q^{48} - 144q^{53} - 20q^{55} + 144q^{56} - 48q^{58} + 64q^{59} + 8q^{60} + 88q^{67} - 176q^{70} + 48q^{71} - 16q^{78} - 144q^{80} - 56q^{81} - 168q^{82} - 88q^{86} + 12q^{88} - 72q^{89} + 120q^{91} - 64q^{92} - 32q^{93} - 72q^{97} - 4q^{99} + O(q^{100}) \)

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.bd.a \(56\) \(3.426\) None \(0\) \(-28\) \(4\) \(0\)
429.2.bd.b \(56\) \(3.426\) None \(0\) \(28\) \(-4\) \(0\)

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

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