Properties

Label 525.2.bm
Level $525$
Weight $2$
Character orbit 525.bm
Rep. character $\chi_{525}(131,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $608$
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.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
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 672 672 0
Cusp forms 608 608 0
Eisenstein series 64 64 0

Trace form

\( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} + O(q^{10}) \) \( 608 q - 9 q^{3} - 78 q^{4} - 36 q^{7} - 3 q^{9} - 30 q^{10} + 3 q^{12} + 16 q^{15} + 50 q^{16} - 8 q^{18} - 18 q^{19} - 21 q^{21} - 24 q^{22} - 66 q^{24} - 10 q^{25} - 30 q^{28} - 7 q^{30} - 36 q^{31} + 36 q^{33} - 100 q^{36} - 14 q^{37} - 31 q^{39} - 30 q^{40} + 20 q^{42} - 96 q^{43} - 117 q^{45} + 42 q^{46} - 28 q^{49} - 8 q^{51} - 66 q^{52} + 3 q^{54} + 48 q^{57} - 38 q^{58} - 49 q^{60} - 18 q^{61} + 4 q^{63} - 32 q^{64} - 3 q^{66} - 22 q^{67} - 270 q^{70} + 45 q^{72} + 102 q^{73} + 135 q^{75} + 58 q^{78} - 34 q^{79} - 55 q^{81} + 108 q^{82} - 75 q^{84} - 96 q^{85} - 9 q^{87} + 36 q^{88} + 38 q^{91} - 22 q^{93} + 30 q^{94} - 81 q^{96} + 36 q^{99} + O(q^{100}) \)

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.bm.a 525.bm 525.am $608$ $4.192$ None \(0\) \(-9\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{30}]$