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Properties

Label 285.2.u
Level $285$
Weight $2$
Character orbit 285.u
Rep. character $\chi_{285}(16,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $84$
Newform subspaces $4$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).

Total New Old
Modular forms 264 84 180
Cusp forms 216 84 132
Eisenstein series 48 0 48

Trace form

\( 84 q + 6 q^{4} + 6 q^{6} + O(q^{10}) \) \( 84 q + 6 q^{4} + 6 q^{6} + 6 q^{10} + 12 q^{12} + 18 q^{13} - 24 q^{14} - 18 q^{16} + 6 q^{19} + 18 q^{21} + 24 q^{22} - 24 q^{23} - 24 q^{24} - 12 q^{26} + 6 q^{27} + 12 q^{28} - 48 q^{29} - 24 q^{31} - 120 q^{32} - 90 q^{34} + 12 q^{35} + 6 q^{36} + 84 q^{38} + 12 q^{40} - 12 q^{41} + 24 q^{42} + 18 q^{43} - 84 q^{44} - 60 q^{46} - 36 q^{47} + 48 q^{48} - 78 q^{49} + 12 q^{51} + 36 q^{52} + 72 q^{53} + 6 q^{54} + 144 q^{56} - 48 q^{58} + 12 q^{59} - 12 q^{60} + 36 q^{61} + 168 q^{62} - 12 q^{63} - 18 q^{64} - 36 q^{65} - 96 q^{66} - 18 q^{67} - 12 q^{68} - 24 q^{69} - 72 q^{70} - 72 q^{71} + 66 q^{73} - 60 q^{74} - 12 q^{75} + 24 q^{76} + 72 q^{77} - 120 q^{78} + 48 q^{79} - 96 q^{80} + 84 q^{82} - 48 q^{83} - 36 q^{84} - 48 q^{85} - 168 q^{86} + 24 q^{88} + 48 q^{89} - 12 q^{90} - 12 q^{91} + 48 q^{92} + 24 q^{96} + 60 q^{97} + 192 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.u.a 285.u 19.e $12$ $2.276$ 12.0.\(\cdots\).1 None \(3\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+\beta _{10}q^{3}+\cdots\)
285.2.u.b 285.u 19.e $18$ $2.276$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-\beta _{2}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
285.2.u.c 285.u 19.e $24$ $2.276$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
285.2.u.d 285.u 19.e $30$ $2.276$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(285, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(285, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)