Properties

Label 285.2.k
Level $285$
Weight $2$
Character orbit 285.k
Rep. character $\chi_{285}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $4$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 88 72 16
Cusp forms 72 72 0
Eisenstein series 16 0 16

Trace form

\( 72 q - 4 q^{3} - 8 q^{6} - 8 q^{7} + O(q^{10}) \) \( 72 q - 4 q^{3} - 8 q^{6} - 8 q^{7} - 8 q^{10} + 16 q^{12} - 16 q^{13} - 16 q^{15} - 72 q^{16} - 8 q^{21} + 24 q^{22} - 24 q^{25} + 8 q^{27} + 8 q^{28} + 16 q^{30} + 16 q^{31} - 16 q^{33} + 8 q^{36} - 24 q^{37} + 24 q^{40} - 64 q^{42} - 16 q^{43} + 32 q^{46} - 12 q^{48} + 24 q^{51} + 72 q^{52} + 16 q^{55} - 72 q^{58} + 36 q^{60} - 64 q^{61} - 8 q^{63} + 40 q^{66} - 56 q^{67} + 64 q^{70} - 20 q^{72} + 40 q^{73} + 40 q^{75} + 16 q^{78} - 24 q^{81} - 88 q^{82} - 8 q^{85} + 168 q^{88} + 40 q^{90} - 32 q^{91} - 8 q^{93} - 48 q^{96} + 8 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.k.a 285.k 15.e $4$ $2.276$ \(\Q(\zeta_{12})\) None 285.2.k.a \(-4\) \(0\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots\)
285.2.k.b 285.k 15.e $4$ $2.276$ \(\Q(\zeta_{12})\) None 285.2.k.a \(4\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
285.2.k.c 285.k 15.e $28$ $2.276$ None 285.2.k.c \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
285.2.k.d 285.k 15.e $36$ $2.276$ None 285.2.k.d \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$