Properties

Label 429.2.m
Level $429$
Weight $2$
Character orbit 429.m
Rep. character $\chi_{429}(109,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $2$
Sturm bound $112$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(i)\)
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 120 56 64
Cusp forms 104 56 48
Eisenstein series 16 0 16

Trace form

\( 56q + 56q^{9} + O(q^{10}) \) \( 56q + 56q^{9} + 4q^{11} + 48q^{14} - 8q^{15} - 72q^{16} - 24q^{20} - 40q^{22} + 8q^{26} + 32q^{31} - 4q^{33} - 16q^{34} - 24q^{37} - 48q^{42} + 12q^{44} - 48q^{47} + 32q^{48} + 32q^{55} - 48q^{58} - 40q^{59} - 8q^{60} + 24q^{66} + 8q^{67} - 40q^{70} - 48q^{71} + 16q^{78} + 48q^{80} + 56q^{81} + 40q^{86} - 72q^{89} - 72q^{91} + 64q^{92} - 16q^{93} + 4q^{99} + O(q^{100}) \)

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

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

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