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Properties

Label 75.3.j
Level $75$
Weight $3$
Character orbit 75.j
Rep. character $\chi_{75}(11,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $72$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.j (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

\( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} + O(q^{10}) \) \( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.3.j.a 75.j 75.j $72$ $2.044$ None \(0\) \(-1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{10}]$