Properties

Label 75.9.j
Level $75$
Weight $9$
Character orbit 75.j
Rep. character $\chi_{75}(11,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $312$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
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: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(75, [\chi])\).

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312 q - 73 q^{3} + 9722 q^{4} - 515 q^{6} - 176 q^{7} + 7907 q^{9} + O(q^{10}) \) \( 312 q - 73 q^{3} + 9722 q^{4} - 515 q^{6} - 176 q^{7} + 7907 q^{9} - 1340 q^{10} - 41153 q^{12} - 47466 q^{13} - 183555 q^{15} - 1375138 q^{16} - 124530 q^{18} - 215676 q^{19} - 322116 q^{21} + 506210 q^{22} - 885600 q^{24} - 2285000 q^{25} + 1668122 q^{27} + 795754 q^{28} + 511395 q^{30} + 137814 q^{31} + 185030 q^{33} - 3354230 q^{34} - 1217933 q^{36} + 8147494 q^{37} + 6148789 q^{39} + 12667680 q^{40} - 20632975 q^{42} + 6373244 q^{43} + 42801695 q^{45} - 5724210 q^{46} + 45688462 q^{48} + 215489176 q^{49} + 4033340 q^{51} + 50335444 q^{52} - 11570780 q^{54} + 1252690 q^{55} + 127383454 q^{57} + 910270 q^{58} + 42215760 q^{60} - 25290306 q^{61} - 103896031 q^{63} + 154389042 q^{64} - 29877340 q^{66} - 47397296 q^{67} + 41856605 q^{69} - 258904800 q^{70} - 239805005 q^{72} - 140624106 q^{73} - 35216050 q^{75} - 212861216 q^{76} + 88431575 q^{78} - 106524466 q^{79} - 142401613 q^{81} - 440177940 q^{82} - 80599906 q^{84} + 255505030 q^{85} - 214355530 q^{87} - 142625130 q^{88} - 76416350 q^{90} - 49394062 q^{91} - 843269096 q^{93} + 501646740 q^{94} - 115465550 q^{96} + 129442874 q^{97} + 136982720 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.9.j.a 75.j 75.j $312$ $30.553$ None \(0\) \(-73\) \(0\) \(-176\) $\mathrm{SU}(2)[C_{10}]$