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Properties

Label 465.2.j
Level $465$
Weight $2$
Character orbit 465.j
Rep. character $\chi_{465}(247,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).

Total New Old
Modular forms 136 64 72
Cusp forms 120 64 56
Eisenstein series 16 0 16

Trace form

\( 64 q + 8 q^{7} - 12 q^{8} + O(q^{10}) \) \( 64 q + 8 q^{7} - 12 q^{8} - 8 q^{10} - 24 q^{16} + 40 q^{20} - 16 q^{25} - 12 q^{28} + 16 q^{31} - 64 q^{32} + 24 q^{33} - 56 q^{36} + 36 q^{38} + 16 q^{40} + 16 q^{41} + 16 q^{47} + 64 q^{50} + 16 q^{51} - 32 q^{56} - 64 q^{62} - 8 q^{63} + 16 q^{66} - 8 q^{67} - 4 q^{70} - 80 q^{71} - 12 q^{72} + 80 q^{76} + 48 q^{80} - 64 q^{81} - 44 q^{82} - 16 q^{87} - 12 q^{90} + 32 q^{93} - 40 q^{95} + 32 q^{97} + 68 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
465.2.j.a 465.j 155.f $64$ $3.713$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(465, [\chi]) \cong \)