Properties

Label 252.4.w
Level $252$
Weight $4$
Character orbit 252.w
Rep. character $\chi_{252}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 300 48 252
Cusp forms 276 48 228
Eisenstein series 24 0 24

Trace form

\( 48q + 6q^{7} + 12q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 12q^{9} + 12q^{11} - 36q^{13} + 66q^{15} - 72q^{17} + 24q^{21} + 30q^{23} - 600q^{25} - 396q^{27} + 42q^{29} + 390q^{35} + 84q^{37} - 840q^{39} - 618q^{41} - 42q^{43} + 366q^{45} + 396q^{47} + 318q^{49} - 738q^{51} - 1620q^{53} + 492q^{57} + 1500q^{59} + 672q^{63} - 588q^{67} - 924q^{69} + 564q^{75} - 2472q^{77} + 1608q^{79} + 2592q^{81} - 360q^{85} + 2640q^{87} + 1722q^{89} + 540q^{91} + 660q^{93} - 792q^{97} - 54q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.4.w.a \(48\) \(14.868\) None \(0\) \(0\) \(0\) \(6\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)