Properties

Label 100.9.h
Level $100$
Weight $9$
Character orbit 100.h
Rep. character $\chi_{100}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
Newform subspaces $1$
Sturm bound $135$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(135\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(100, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 5 q^{2} - 3 q^{4} + 160 q^{5} + 509 q^{6} - 21830 q^{8} - 249324 q^{9} + O(q^{10}) \) \( 472 q - 5 q^{2} - 3 q^{4} + 160 q^{5} + 509 q^{6} - 21830 q^{8} - 249324 q^{9} + 4155 q^{10} - 5 q^{12} - 10 q^{13} - 35241 q^{14} + 194457 q^{16} - 10 q^{17} - 315765 q^{20} - 39372 q^{21} - 674630 q^{22} + 1016144 q^{24} - 124000 q^{25} + 840530 q^{26} - 327685 q^{28} - 68886 q^{29} - 2410045 q^{30} - 10 q^{33} - 1593235 q^{34} + 2844341 q^{36} + 7566990 q^{37} + 10916995 q^{38} + 1665050 q^{40} + 5468394 q^{41} - 36609835 q^{42} + 510580 q^{44} - 4274700 q^{45} - 1721391 q^{46} + 27274970 q^{48} + 348414536 q^{49} + 4672165 q^{50} - 92260780 q^{52} + 15636590 q^{53} - 13767487 q^{54} - 7138896 q^{56} + 105499870 q^{58} - 88218440 q^{60} + 15307594 q^{61} - 82821380 q^{62} - 13937508 q^{64} - 77435650 q^{65} + 63249730 q^{66} - 73645122 q^{69} - 20098010 q^{70} + 238689175 q^{72} - 10 q^{73} - 24707620 q^{74} + 18918920 q^{76} - 57648020 q^{77} + 273881375 q^{78} + 340504710 q^{80} - 349779960 q^{81} - 412235262 q^{84} + 56543390 q^{85} + 340843779 q^{86} + 756329470 q^{88} - 296838366 q^{89} + 660374295 q^{90} + 85285570 q^{92} - 507069831 q^{94} + 640257404 q^{96} + 656715990 q^{97} - 285677340 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.9.h.a 100.h 100.h $472$ $40.738$ None 100.9.h.a \(-5\) \(0\) \(160\) \(0\) $\mathrm{SU}(2)[C_{10}]$