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

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

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.j.a \(72\) \(2.044\) None \(0\) \(-1\) \(0\) \(-8\)