Properties

Label 100.9.j
Level $100$
Weight $9$
Character orbit 100.j
Rep. character $\chi_{100}(11,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
Newform subspaces $2$
Sturm bound $135$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(135\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

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

\( 472 q - 3 q^{2} - 3 q^{4} - 176 q^{5} - 515 q^{6} + 13092 q^{8} + 249312 q^{9} + O(q^{10}) \) \( 472 q - 3 q^{2} - 3 q^{4} - 176 q^{5} - 515 q^{6} + 13092 q^{8} + 249312 q^{9} + 20309 q^{10} - 35805 q^{12} - 28566 q^{13} - 33705 q^{14} - 194463 q^{16} - 193206 q^{17} + 270112 q^{18} + 165639 q^{20} + 39360 q^{21} + 140220 q^{22} + 989900 q^{24} - 761376 q^{25} - 840546 q^{26} - 2358605 q^{28} - 68886 q^{29} + 7229675 q^{30} + 1309942 q^{32} - 1866570 q^{33} - 1592211 q^{34} - 2582203 q^{36} - 4540206 q^{37} + 4012465 q^{38} + 162354 q^{40} - 5468406 q^{41} - 21337315 q^{42} + 510580 q^{44} + 9511344 q^{45} + 1721385 q^{46} + 41153690 q^{48} - 349949928 q^{49} - 65290371 q^{50} - 8175176 q^{52} - 2144526 q^{53} - 13729145 q^{54} + 7138890 q^{56} - 19745300 q^{57} + 3606634 q^{58} + 96768050 q^{60} - 15307606 q^{61} - 87505940 q^{62} - 13937508 q^{64} + 118747458 q^{65} - 69968200 q^{66} + 32716254 q^{68} - 73697610 q^{69} + 39639840 q^{70} - 199742063 q^{72} + 70429514 q^{73} - 24706596 q^{74} - 19181080 q^{76} + 111211200 q^{77} - 197089615 q^{78} - 326606016 q^{80} - 625945728 q^{81} + 72505754 q^{82} - 377672700 q^{84} + 76354258 q^{85} - 340843785 q^{86} - 29231040 q^{88} - 296838366 q^{89} + 461930399 q^{90} + 43044280 q^{92} + 241823660 q^{93} - 442380075 q^{94} - 474931550 q^{96} + 349148394 q^{97} + 25202232 q^{98} + O(q^{100}) \)

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.j.a 100.j 100.j $8$ $40.738$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) 100.9.j.a \(-32\) \(0\) \(1054\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(-2^{4}+2^{4}\zeta_{20}^{2}-2^{4}\zeta_{20}^{4}+2^{4}\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.9.j.b 100.j 100.j $464$ $40.738$ None 100.9.j.b \(29\) \(0\) \(-1230\) \(0\) $\mathrm{SU}(2)[C_{10}]$