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Properties

Label 459.2.f
Level $459$
Weight $2$
Character orbit 459.f
Rep. character $\chi_{459}(55,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $3$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 459 = 3^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 459.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(459, [\chi])\).

Total New Old
Modular forms 120 48 72
Cusp forms 96 48 48
Eisenstein series 24 0 24

Trace form

\( 48 q - 48 q^{4} + 20 q^{10} + 4 q^{13} + 56 q^{16} - 4 q^{22} + 4 q^{28} - 4 q^{31} + 32 q^{34} - 60 q^{37} - 104 q^{40} + 36 q^{46} + 8 q^{52} + 4 q^{55} - 32 q^{58} - 52 q^{61} - 40 q^{64} + 16 q^{67}+ \cdots - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(459, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
459.2.f.a 459.f 17.c $4$ $3.665$ \(\Q(\zeta_{8})\) None 459.2.f.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+4\zeta_{8}q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
459.2.f.b 459.f 17.c $20$ $3.665$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 459.2.f.b \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{10}q^{2}+(-1-\beta _{4})q^{4}-\beta _{17}q^{5}+\cdots\)
459.2.f.c 459.f 17.c $24$ $3.665$ None 459.2.f.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(459, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(459, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)