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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(429, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
429.2.bd.a 429.bd 143.o $56$ $3.426$ None \(0\) \(-28\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$
429.2.bd.b 429.bd 143.o $56$ $3.426$ None \(0\) \(28\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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