Properties

Label 100.4.l
Level $100$
Weight $4$
Character orbit 100.l
Rep. character $\chi_{100}(3,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $344$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(100, [\chi])\).

Total New Old
Modular forms 376 376 0
Cusp forms 344 344 0
Eisenstein series 32 32 0

Trace form

\( 344 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 6 q^{6} + 34 q^{8} - 20 q^{9} + O(q^{10}) \) \( 344 q - 8 q^{2} - 10 q^{4} - 16 q^{5} - 6 q^{6} + 34 q^{8} - 20 q^{9} + 64 q^{10} + 70 q^{12} - 62 q^{13} - 10 q^{14} - 6 q^{16} + 114 q^{17} - 316 q^{18} - 326 q^{20} - 12 q^{21} - 370 q^{22} - 126 q^{25} - 16 q^{26} + 870 q^{28} - 20 q^{29} + 1230 q^{30} + 622 q^{32} - 100 q^{33} - 10 q^{34} - 262 q^{36} - 346 q^{37} + 880 q^{38} + 204 q^{40} - 12 q^{41} - 470 q^{42} - 1340 q^{44} - 606 q^{45} - 6 q^{46} - 3400 q^{48} - 2206 q^{50} - 2356 q^{52} + 678 q^{53} - 3780 q^{54} - 6 q^{56} + 940 q^{57} - 1112 q^{58} + 2810 q^{60} - 12 q^{61} + 2900 q^{62} + 4820 q^{64} + 1758 q^{65} - 870 q^{66} + 2418 q^{68} - 20 q^{69} + 3030 q^{70} + 1892 q^{72} - 1962 q^{73} + 240 q^{76} - 3140 q^{77} - 3460 q^{78} - 2106 q^{80} + 4362 q^{81} - 8826 q^{82} - 11290 q^{84} + 3248 q^{85} - 6 q^{86} - 1570 q^{88} + 1410 q^{89} + 3494 q^{90} + 6130 q^{92} - 1300 q^{93} + 11030 q^{94} - 1746 q^{96} - 12626 q^{97} + 13324 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.4.l.a 100.l 100.l $8$ $5.900$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{20}]$ \(q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots\)
100.4.l.b 100.l 100.l $336$ $5.900$ None \(-4\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{20}]$