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Properties

Label 56.4.m
Level $56$
Weight $4$
Character orbit 56.m
Rep. character $\chi_{56}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 56.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(56, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 4 q^{8} + 160 q^{9} + O(q^{10}) \) \( 44 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 4 q^{8} + 160 q^{9} - 12 q^{10} - 22 q^{11} + 162 q^{12} - 172 q^{14} - 48 q^{16} - 6 q^{17} + 122 q^{18} - 6 q^{19} - 92 q^{22} - 354 q^{24} - 352 q^{25} - 402 q^{26} - 734 q^{28} - 50 q^{30} + 528 q^{32} - 6 q^{33} + 18 q^{35} - 400 q^{36} + 1614 q^{38} - 798 q^{40} + 1222 q^{42} + 800 q^{43} - 390 q^{44} - 616 q^{46} + 356 q^{49} + 160 q^{50} - 810 q^{51} + 2208 q^{52} + 1170 q^{54} + 1504 q^{56} + 220 q^{57} + 558 q^{58} - 2070 q^{59} - 602 q^{60} + 1912 q^{64} - 252 q^{65} - 3138 q^{66} - 98 q^{67} + 3048 q^{68} - 1992 q^{70} + 128 q^{72} + 642 q^{73} + 566 q^{74} + 744 q^{75} - 5220 q^{78} - 3276 q^{80} + 182 q^{81} - 2430 q^{82} - 2360 q^{84} + 1256 q^{86} - 770 q^{88} - 1278 q^{89} - 424 q^{91} - 5900 q^{92} - 246 q^{94} - 5652 q^{96} + 3564 q^{98} + 1000 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(56, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
56.4.m.a 56.m 56.m $44$ $3.304$ None \(-2\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$