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Properties

Label 201.3.h
Level $201$
Weight $3$
Character orbit 201.h
Rep. character $\chi_{201}(97,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $46$
Newform subspaces $2$
Sturm bound $68$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(68\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(201, [\chi])\).

Total New Old
Modular forms 94 46 48
Cusp forms 86 46 40
Eisenstein series 8 0 8

Trace form

\( 46 q + 60 q^{4} + 6 q^{7} - 138 q^{9} + O(q^{10}) \) \( 46 q + 60 q^{4} + 6 q^{7} - 138 q^{9} + 36 q^{10} + 42 q^{11} + 24 q^{12} + 3 q^{13} + 12 q^{14} - 12 q^{15} - 156 q^{16} - 4 q^{17} + 40 q^{19} + 96 q^{20} - 36 q^{21} - 68 q^{22} - 14 q^{23} - 36 q^{24} - 278 q^{25} + 100 q^{26} + 114 q^{28} + 42 q^{29} - 72 q^{30} + 27 q^{31} - 138 q^{32} + 18 q^{33} + 48 q^{34} - 90 q^{35} - 180 q^{36} - 20 q^{37} - 102 q^{38} + 57 q^{39} + 356 q^{40} - 174 q^{41} + 180 q^{44} + 144 q^{46} - 166 q^{47} + 120 q^{48} + 255 q^{49} - 138 q^{50} - 36 q^{51} - 268 q^{55} + 236 q^{56} - 114 q^{57} + 20 q^{59} - 120 q^{60} + 183 q^{61} + 132 q^{62} - 18 q^{63} - 560 q^{64} + 116 q^{65} + 69 q^{67} + 164 q^{68} + 36 q^{69} + 128 q^{71} + 171 q^{73} + 1290 q^{74} - 4 q^{76} - 432 q^{77} - 126 q^{78} - 615 q^{79} + 318 q^{80} + 414 q^{81} - 316 q^{82} - 50 q^{83} + 264 q^{84} + 390 q^{85} + 862 q^{86} - 126 q^{87} - 356 q^{88} + 208 q^{89} - 108 q^{90} + 304 q^{91} + 420 q^{92} + 213 q^{93} + 1350 q^{95} - 72 q^{96} - 525 q^{97} - 306 q^{98} - 126 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(201, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
201.3.h.a 201.h 67.d $22$ $5.477$ None \(0\) \(0\) \(0\) \(-15\) $\mathrm{SU}(2)[C_{6}]$
201.3.h.b 201.h 67.d $24$ $5.477$ None \(0\) \(0\) \(0\) \(21\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(201, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(201, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)