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Properties

Label 475.3.s
Level $475$
Weight $3$
Character orbit 475.s
Rep. character $\chi_{475}(51,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $360$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.s (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(150\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(475, [\chi])\).

Total New Old
Modular forms 636 396 240
Cusp forms 564 360 204
Eisenstein series 72 36 36

Trace form

\( 360 q + 6 q^{2} + 12 q^{3} - 12 q^{6} - 6 q^{7} + 9 q^{8} - 12 q^{9} + O(q^{10}) \) \( 360 q + 6 q^{2} + 12 q^{3} - 12 q^{6} - 6 q^{7} + 9 q^{8} - 12 q^{9} + 6 q^{11} + 81 q^{12} + 33 q^{13} + 39 q^{14} - 12 q^{16} + 63 q^{17} - 24 q^{19} - 72 q^{21} - 138 q^{22} + 42 q^{23} - 33 q^{26} - 9 q^{27} - 396 q^{28} + 99 q^{29} + 81 q^{31} + 135 q^{32} - 354 q^{33} + 96 q^{34} + 201 q^{36} - 30 q^{38} - 36 q^{39} - 228 q^{41} - 441 q^{42} + 405 q^{43} - 63 q^{44} - 792 q^{46} + 249 q^{47} + 1197 q^{48} - 834 q^{49} - 270 q^{51} + 81 q^{52} + 105 q^{53} + 45 q^{54} + 306 q^{57} + 36 q^{58} + 99 q^{59} + 456 q^{61} - 828 q^{62} + 240 q^{63} + 561 q^{64} + 1284 q^{66} - 693 q^{67} - 360 q^{68} - 774 q^{69} + 720 q^{71} - 390 q^{72} - 240 q^{73} + 75 q^{74} + 342 q^{76} - 282 q^{77} - 591 q^{78} - 471 q^{79} - 1365 q^{81} + 759 q^{82} + 36 q^{83} - 99 q^{84} - 1164 q^{86} + 315 q^{87} - 1467 q^{88} + 282 q^{89} - 909 q^{91} + 468 q^{92} - 951 q^{93} - 810 q^{96} + 897 q^{97} + 1287 q^{98} + 1284 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)