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Properties

Label 232.4.s
Level $232$
Weight $4$
Character orbit 232.s
Rep. character $\chi_{232}(45,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $528$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 232.s (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 232 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(232, [\chi])\).

Total New Old
Modular forms 552 552 0
Cusp forms 528 528 0
Eisenstein series 24 24 0

Trace form

\( 528 q - 3 q^{2} + 5 q^{4} - 51 q^{6} + 18 q^{7} - 24 q^{8} + 746 q^{9} + O(q^{10}) \) \( 528 q - 3 q^{2} + 5 q^{4} - 51 q^{6} + 18 q^{7} - 24 q^{8} + 746 q^{9} - 21 q^{10} + 12 q^{12} + 81 q^{14} - 118 q^{15} - 155 q^{16} + 28 q^{17} - 914 q^{18} - 287 q^{20} - 472 q^{22} + 594 q^{23} + 17 q^{24} + 2034 q^{25} - 101 q^{26} + 256 q^{28} + 302 q^{30} - 10 q^{31} - 358 q^{32} - 118 q^{33} - 279 q^{34} + 318 q^{36} - 1934 q^{38} - 1618 q^{39} + 323 q^{40} + 212 q^{41} - 2132 q^{42} - 1192 q^{44} + 4652 q^{46} - 10 q^{47} + 544 q^{48} - 3734 q^{49} + 258 q^{50} + 4214 q^{52} - 1778 q^{54} - 510 q^{55} + 2759 q^{56} - 132 q^{57} - 3955 q^{58} + 7050 q^{60} + 2287 q^{62} - 6 q^{63} - 298 q^{64} - 420 q^{65} + 2315 q^{66} - 904 q^{68} + 10686 q^{70} + 498 q^{71} - 693 q^{72} - 1860 q^{73} + 766 q^{74} - 3657 q^{76} + 3125 q^{78} - 1510 q^{79} - 2224 q^{80} - 4718 q^{81} + 2362 q^{82} + 961 q^{84} - 4520 q^{86} - 2738 q^{87} - 630 q^{88} - 1078 q^{89} + 5748 q^{90} - 478 q^{92} - 5610 q^{94} - 510 q^{95} - 256 q^{96} + 772 q^{97} + 1430 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(232, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
232.4.s.a 232.s 232.s $528$ $13.688$ None \(-3\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{14}]$