Properties

Label 201.4.e
Level $201$
Weight $4$
Character orbit 201.e
Rep. character $\chi_{201}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $68$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(201, [\chi])\).

Total New Old
Modular forms 140 68 72
Cusp forms 132 68 64
Eisenstein series 8 0 8

Trace form

\( 68 q + 4 q^{2} - 12 q^{3} - 156 q^{4} + 8 q^{7} + 156 q^{8} + 612 q^{9} + O(q^{10}) \) \( 68 q + 4 q^{2} - 12 q^{3} - 156 q^{4} + 8 q^{7} + 156 q^{8} + 612 q^{9} + 12 q^{10} + 72 q^{12} + 42 q^{13} + 228 q^{14} + 24 q^{15} - 644 q^{16} + 44 q^{17} + 36 q^{18} - 156 q^{19} - 16 q^{20} - 108 q^{21} - 292 q^{22} + 56 q^{23} + 180 q^{24} + 1604 q^{25} + 20 q^{26} - 108 q^{27} - 906 q^{28} + 124 q^{29} - 48 q^{30} + 790 q^{31} - 810 q^{32} + 96 q^{33} + 164 q^{34} - 720 q^{35} - 1404 q^{36} - 740 q^{37} - 174 q^{38} + 402 q^{39} - 1156 q^{40} - 384 q^{41} + 600 q^{42} - 1692 q^{43} - 512 q^{44} - 48 q^{46} + 420 q^{47} + 144 q^{48} - 66 q^{49} - 166 q^{50} + 180 q^{51} + 296 q^{52} + 1576 q^{53} + 1060 q^{55} - 876 q^{56} + 456 q^{57} - 4792 q^{58} + 1920 q^{59} + 1032 q^{60} - 222 q^{61} - 9692 q^{62} + 72 q^{63} + 5968 q^{64} - 1452 q^{65} - 2160 q^{66} - 1054 q^{67} + 2540 q^{68} + 792 q^{69} + 2540 q^{70} + 812 q^{71} + 1404 q^{72} - 846 q^{73} - 570 q^{74} - 1380 q^{75} + 1492 q^{76} + 636 q^{77} + 2058 q^{78} + 2542 q^{79} + 4770 q^{80} + 5508 q^{81} + 2156 q^{82} + 1180 q^{83} + 120 q^{84} + 2504 q^{85} + 1010 q^{86} - 84 q^{87} + 100 q^{88} - 256 q^{89} + 108 q^{90} + 4320 q^{91} + 4348 q^{92} - 618 q^{93} - 12748 q^{94} + 1576 q^{95} - 720 q^{96} - 498 q^{97} + 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.4.e.a 201.e 67.c $32$ $11.859$ None \(2\) \(96\) \(4\) \(-14\) $\mathrm{SU}(2)[C_{3}]$
201.4.e.b 201.e 67.c $36$ $11.859$ None \(2\) \(-108\) \(-4\) \(22\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)