Properties

 Label 75.3.h Level $75$ Weight $3$ Character orbit 75.h Rep. character $\chi_{75}(14,\cdot)$ Character field $\Q(\zeta_{10})$ Dimension $72$ Newform subspaces $1$ Sturm bound $30$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 75.h (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$75$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$30$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(75, [\chi])$$.

Total New Old
Modular forms 88 88 0
Cusp forms 72 72 0
Eisenstein series 16 16 0

Trace form

 $$72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} + O(q^{10})$$ $$72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30} - 126 q^{31} + 20 q^{33} + 210 q^{34} - 213 q^{36} + 110 q^{37} - 191 q^{39} + 140 q^{40} - 175 q^{42} - 405 q^{45} - 210 q^{46} + 150 q^{48} - 224 q^{49} - 60 q^{51} - 320 q^{52} + 320 q^{54} - 10 q^{55} - 70 q^{58} + 1190 q^{60} + 294 q^{61} + 795 q^{63} + 362 q^{64} - 470 q^{66} - 260 q^{67} + 335 q^{69} + 1200 q^{70} + 215 q^{72} - 150 q^{73} + 200 q^{75} - 16 q^{76} - 1295 q^{78} - 346 q^{79} + 507 q^{81} - 456 q^{84} - 1450 q^{85} - 430 q^{87} - 1710 q^{88} - 820 q^{90} + 538 q^{91} - 560 q^{94} + 740 q^{96} - 150 q^{97} + 60 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(75, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.3.h.a $72$ $2.044$ None $$0$$ $$-5$$ $$0$$ $$0$$