Properties

Label 90.3.j
Level $90$
Weight $3$
Character orbit 90.j
Rep. character $\chi_{90}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 90.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(90, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24 q - 24 q^{4} + 18 q^{5} - 8 q^{6} + 20 q^{9} + O(q^{10}) \) \( 24 q - 24 q^{4} + 18 q^{5} - 8 q^{6} + 20 q^{9} + 36 q^{11} - 36 q^{14} - 26 q^{15} - 48 q^{16} - 36 q^{20} + 112 q^{21} + 8 q^{24} - 6 q^{25} + 36 q^{29} + 4 q^{30} - 60 q^{31} - 104 q^{36} - 348 q^{39} - 144 q^{41} + 242 q^{45} - 24 q^{46} + 108 q^{49} + 288 q^{50} + 64 q^{51} + 260 q^{54} - 156 q^{55} + 72 q^{56} - 36 q^{59} + 20 q^{60} + 48 q^{61} + 192 q^{64} - 414 q^{65} + 272 q^{66} + 236 q^{69} + 48 q^{70} + 144 q^{74} - 370 q^{75} + 132 q^{79} - 824 q^{81} + 8 q^{84} + 48 q^{85} - 432 q^{86} + 112 q^{90} + 168 q^{91} - 84 q^{94} + 540 q^{95} + 16 q^{96} + 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
90.3.j.a 90.j 45.h $8$ $2.452$ \(\Q(\zeta_{24})\) None 90.3.j.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{4}q^{2}+3\zeta_{24}q^{3}+(-2+2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
90.3.j.b 90.j 45.h $16$ $2.452$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 90.3.j.b \(0\) \(0\) \(30\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)