↑

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 $0$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.4.l.a 252.l 63.g $48$ $14.868$ None \(0\) \(0\) \(-40\) \(-6\) $\mathrm{SU}(2)[C_{3}]$

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

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