Properties

Label 90.3.k
Level $90$
Weight $3$
Character orbit 90.k
Rep. character $\chi_{90}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $48$
Newform subspaces $2$
Sturm bound $54$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 90.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 160 48 112
Cusp forms 128 48 80
Eisenstein series 32 0 32

Trace form

\( 48 q + 4 q^{3} + 16 q^{6} + O(q^{10}) \) \( 48 q + 4 q^{3} + 16 q^{6} - 24 q^{11} + 8 q^{12} + 4 q^{15} + 96 q^{16} - 72 q^{17} - 32 q^{18} + 24 q^{20} - 32 q^{21} - 120 q^{23} + 12 q^{25} + 172 q^{27} - 96 q^{30} - 116 q^{33} - 576 q^{35} - 80 q^{36} + 168 q^{37} - 72 q^{38} - 160 q^{42} - 28 q^{45} - 48 q^{46} + 12 q^{47} + 32 q^{48} + 96 q^{50} + 488 q^{51} + 768 q^{53} - 264 q^{55} + 48 q^{56} + 340 q^{57} - 48 q^{58} + 88 q^{60} - 96 q^{61} + 288 q^{62} + 4 q^{63} + 408 q^{65} + 160 q^{66} + 156 q^{67} - 72 q^{68} + 48 q^{71} + 128 q^{72} - 652 q^{75} - 96 q^{77} - 504 q^{78} - 64 q^{81} - 96 q^{82} - 624 q^{83} + 96 q^{85} + 432 q^{86} - 584 q^{87} + 112 q^{90} - 336 q^{91} - 240 q^{92} + 760 q^{93} + 696 q^{95} + 32 q^{96} - 396 q^{97} + 288 q^{98} + O(q^{100}) \)

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.k.a 90.k 45.k $24$ $2.452$ None 90.3.k.a \(-12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
90.3.k.b 90.k 45.k $24$ $2.452$ None 90.3.k.b \(12\) \(4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$

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

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