Properties

Label 252.4.l
Level $252$
Weight $4$
Character orbit 252.l
Rep. character $\chi_{252}(193,\cdot)$
Character field $\Q(\zeta_{3})$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 48q - 40q^{5} - 6q^{7} - 2q^{9} + O(q^{10}) \) \( 48q - 40q^{5} - 6q^{7} - 2q^{9} - 8q^{11} - 12q^{13} - 26q^{15} + 112q^{17} + 60q^{19} - 182q^{21} - 20q^{23} + 1200q^{25} + 194q^{29} - 30q^{31} + 380q^{33} + 394q^{35} - 84q^{37} + 10q^{39} + 210q^{41} + 42q^{43} + 386q^{45} + 66q^{47} + 516q^{49} - 640q^{51} - 468q^{53} + 612q^{55} + 1476q^{57} + 458q^{59} + 402q^{61} + 1518q^{63} - 828q^{65} + 294q^{67} - 28q^{69} - 2228q^{71} - 336q^{73} - 3338q^{75} - 1120q^{77} + 384q^{79} - 890q^{81} + 1024q^{83} + 360q^{85} - 1508q^{87} + 2922q^{89} - 120q^{91} + 1312q^{93} - 1214q^{95} - 264q^{97} - 2246q^{99} + O(q^{100}) \)

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.l.a \(48\) \(14.868\) None \(0\) \(0\) \(-40\) \(-6\)

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

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