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Properties

Label 475.3.z
Level $475$
Weight $3$
Character orbit 475.z
Rep. character $\chi_{475}(69,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $784$
Sturm bound $150$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 475.z (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(150\)

Dimensions

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

Total New Old
Modular forms 816 816 0
Cusp forms 784 784 0
Eisenstein series 32 32 0

Trace form

\( 784 q - 15 q^{2} - 15 q^{3} + 189 q^{4} - 3 q^{5} - 19 q^{6} + 279 q^{9} + O(q^{10}) \) \( 784 q - 15 q^{2} - 15 q^{3} + 189 q^{4} - 3 q^{5} - 19 q^{6} + 279 q^{9} - 39 q^{10} - 42 q^{11} - 15 q^{13} - 63 q^{14} + 111 q^{15} + 373 q^{16} - 40 q^{17} + 24 q^{19} - 8 q^{20} + 72 q^{21} - 135 q^{22} + 65 q^{23} + 24 q^{24} + 51 q^{25} - 148 q^{26} + 75 q^{28} - 99 q^{29} + 256 q^{30} - 285 q^{33} - 9 q^{34} + 181 q^{35} + 467 q^{36} - 655 q^{38} - 288 q^{39} + 636 q^{40} - 9 q^{41} + 175 q^{42} - 277 q^{44} + 768 q^{45} - 115 q^{47} - 15 q^{48} - 4948 q^{49} + 126 q^{51} - 75 q^{52} - 15 q^{53} - 286 q^{54} - 114 q^{55} + 370 q^{58} - 369 q^{59} + 1044 q^{60} + 87 q^{61} + 320 q^{62} + 1025 q^{63} - 1426 q^{64} - 143 q^{66} - 15 q^{67} + 684 q^{70} + 156 q^{71} - 1350 q^{72} + 315 q^{73} - 210 q^{74} - 216 q^{76} + 920 q^{77} - 150 q^{78} - 189 q^{79} + 167 q^{80} - 47 q^{81} + 590 q^{83} - 166 q^{85} + 441 q^{86} - 2790 q^{87} - 99 q^{89} - 1755 q^{90} + 432 q^{91} + 1065 q^{92} - 448 q^{95} + 1270 q^{96} + 120 q^{97} + 1140 q^{98} + 48 q^{99} + O(q^{100}) \)

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.