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Properties

Label 525.2.bv
Level $525$
Weight $2$
Character orbit 525.bv
Rep. character $\chi_{525}(52,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $640$
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.bv (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
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 1344 640 704
Cusp forms 1216 640 576
Eisenstein series 128 0 128

Trace form

\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + O(q^{10}) \) \( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bv.a 525.bv 175.x $640$ $4.192$ None \(0\) \(0\) \(12\) \(-8\) $\mathrm{SU}(2)[C_{60}]$

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)