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Properties

Label 265.2.j
Level $265$
Weight $2$
Character orbit 265.j
Rep. character $\chi_{265}(83,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $50$
Newform subspaces $2$
Sturm bound $54$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 265 = 5 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 265.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 265 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(54\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(265, [\chi])\).

Total New Old
Modular forms 58 58 0
Cusp forms 50 50 0
Eisenstein series 8 8 0

Trace form

\( 50 q - 2 q^{2} + 38 q^{4} - 2 q^{5} - 6 q^{8} - 42 q^{9} - 4 q^{10} + 2 q^{13} - 4 q^{14} - 12 q^{15} + 6 q^{16} + 14 q^{17} - 10 q^{18} + 4 q^{19} - 18 q^{20} - 4 q^{21} - 8 q^{23} + 34 q^{25} - 2 q^{26}+ \cdots + 42 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(265, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
265.2.j.a 265.j 265.j $2$ $2.116$ \(\Q(\sqrt{-1}) \) None 265.2.e.a \(2\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+2 i q^{3}-q^{4}+(2 i-1)q^{5}+\cdots\)
265.2.j.b 265.j 265.j $48$ $2.116$ None 265.2.e.b \(-4\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$