Properties

Label 525.2.bk
Level $525$
Weight $2$
Character orbit 525.bk
Rep. character $\chi_{525}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 672 480 192
Cusp forms 608 480 128
Eisenstein series 64 0 64

Trace form

\( 480 q + 4 q^{3} + O(q^{10}) \) \( 480 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} + 16 q^{15} + 120 q^{16} + 20 q^{18} - 40 q^{19} - 48 q^{22} - 104 q^{25} + 16 q^{27} - 20 q^{30} - 28 q^{33} - 80 q^{34} + 16 q^{37} - 40 q^{39} - 64 q^{40} - 80 q^{42} + 40 q^{43} - 20 q^{45} - 276 q^{48} - 260 q^{54} - 40 q^{55} - 4 q^{57} - 40 q^{58} - 52 q^{60} - 32 q^{63} + 160 q^{64} + 56 q^{67} + 8 q^{70} + 288 q^{72} + 48 q^{73} + 60 q^{75} + 140 q^{78} + 80 q^{79} - 40 q^{81} - 184 q^{85} + 96 q^{87} - 56 q^{88} + 24 q^{90} + 96 q^{93} - 560 q^{94} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.2.bk.a 525.bk 75.l $480$ $4.192$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)