Properties

Label 90.3.h
Level $90$
Weight $3$
Character orbit 90.h
Rep. character $\chi_{90}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 90.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 64 16 48
Eisenstein series 16 0 16

Trace form

\( 16 q - 4 q^{3} + 16 q^{4} + 16 q^{6} - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{3} + 16 q^{4} + 16 q^{6} - 4 q^{7} - 4 q^{9} - 16 q^{12} + 20 q^{13} - 36 q^{14} - 20 q^{15} - 32 q^{16} + 16 q^{18} + 80 q^{19} - 44 q^{21} + 24 q^{22} + 108 q^{23} - 8 q^{24} + 40 q^{25} - 124 q^{27} - 16 q^{28} - 72 q^{29} + 20 q^{30} - 16 q^{31} - 264 q^{33} - 48 q^{34} + 32 q^{36} - 88 q^{37} - 72 q^{38} - 8 q^{39} + 108 q^{41} + 128 q^{42} + 92 q^{43} - 80 q^{45} + 24 q^{46} + 216 q^{47} - 16 q^{48} - 84 q^{49} + 168 q^{51} - 40 q^{52} + 148 q^{54} - 72 q^{56} + 28 q^{57} + 144 q^{59} + 40 q^{60} - 76 q^{61} - 104 q^{63} - 128 q^{64} + 180 q^{65} + 96 q^{66} + 56 q^{67} + 72 q^{68} - 72 q^{69} + 60 q^{70} + 64 q^{72} + 416 q^{73} - 288 q^{74} + 20 q^{75} + 80 q^{76} - 684 q^{77} + 56 q^{78} + 80 q^{79} + 320 q^{81} - 192 q^{82} + 396 q^{83} + 40 q^{84} - 60 q^{85} - 216 q^{86} + 420 q^{87} - 48 q^{88} - 160 q^{90} - 656 q^{91} + 216 q^{92} - 356 q^{93} - 84 q^{94} - 360 q^{95} - 80 q^{96} - 16 q^{97} + 816 q^{99} + O(q^{100}) \)

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.h.a 90.h 9.d $16$ $2.452$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 90.3.h.a \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{3}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)