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Properties

Label 525.2.bp
Level $525$
Weight $2$
Character orbit 525.bp
Rep. character $\chi_{525}(59,\cdot)$
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.bp (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

\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} + O(q^{10}) \) \( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99} + O(q^{100}) \)

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.bp.a 525.bp 525.ap $608$ $4.192$ None \(0\) \(-15\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$