Properties

Label 100.3.j
Level $100$
Weight $3$
Character orbit 100.j
Rep. character $\chi_{100}(11,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $112$
Newform subspaces $1$
Sturm bound $45$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 100.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(100, [\chi])\).

Total New Old
Modular forms 128 128 0
Cusp forms 112 112 0
Eisenstein series 16 16 0

Trace form

\( 112 q - 3 q^{2} - 3 q^{4} - 10 q^{5} - 11 q^{6} - 12 q^{8} + 66 q^{9} + O(q^{10}) \) \( 112 q - 3 q^{2} - 3 q^{4} - 10 q^{5} - 11 q^{6} - 12 q^{8} + 66 q^{9} + 5 q^{10} - 45 q^{12} + 6 q^{13} - 21 q^{14} - 63 q^{16} + 14 q^{17} - 32 q^{18} - 25 q^{20} + 48 q^{21} + 44 q^{24} - 30 q^{25} - 50 q^{26} + 115 q^{28} - 26 q^{29} - 85 q^{30} - 138 q^{32} - 90 q^{33} - 75 q^{34} - 139 q^{36} + 24 q^{37} + 65 q^{38} - 270 q^{40} + 94 q^{41} - 55 q^{42} - 140 q^{44} + 30 q^{45} - 111 q^{46} - 70 q^{48} - 384 q^{49} - 195 q^{50} + 424 q^{52} + 96 q^{53} + 283 q^{54} + 234 q^{56} - 20 q^{57} + 406 q^{58} + 50 q^{60} - 106 q^{61} + 400 q^{62} + 252 q^{64} - 180 q^{65} + 260 q^{66} + 126 q^{68} - 282 q^{69} + 240 q^{70} + 337 q^{72} - 274 q^{73} + 100 q^{74} - 40 q^{76} + 240 q^{77} - 595 q^{78} + 360 q^{80} - 390 q^{81} + 554 q^{82} + 708 q^{84} - 200 q^{85} + 459 q^{86} - 396 q^{89} + 515 q^{90} - 120 q^{92} - 100 q^{93} + 429 q^{94} + 634 q^{96} + 54 q^{97} + 188 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.3.j.a 100.j 100.j $112$ $2.725$ None \(-3\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{10}]$