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Properties

Label 525.2.bg
Level $525$
Weight $2$
Character orbit 525.bg
Rep. character $\chi_{525}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $320$
Newform subspaces $2$
Sturm bound $160$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

Trace form

\( 320 q + 40 q^{4} - 2 q^{5} - 8 q^{6} + 8 q^{7} - 36 q^{8} + 40 q^{9} + O(q^{10}) \) \( 320 q + 40 q^{4} - 2 q^{5} - 8 q^{6} + 8 q^{7} - 36 q^{8} + 40 q^{9} - 8 q^{10} + 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 12 q^{17} + 16 q^{19} - 8 q^{20} + 32 q^{22} + 12 q^{23} - 48 q^{24} - 70 q^{28} + 24 q^{29} + 16 q^{30} + 30 q^{31} - 24 q^{32} - 12 q^{33} - 16 q^{35} - 80 q^{36} - 4 q^{37} + 2 q^{38} - 12 q^{40} - 36 q^{41} + 14 q^{42} - 136 q^{43} - 16 q^{44} - 2 q^{45} - 32 q^{46} - 4 q^{47} + 32 q^{48} + 16 q^{49} - 148 q^{50} - 6 q^{52} - 60 q^{53} + 4 q^{54} + 16 q^{55} - 16 q^{57} - 24 q^{58} + 24 q^{59} + 26 q^{60} + 20 q^{61} - 216 q^{62} - 14 q^{63} - 164 q^{64} + 10 q^{65} + 16 q^{66} + 36 q^{67} - 12 q^{68} - 32 q^{69} - 32 q^{71} + 18 q^{72} + 44 q^{73} - 12 q^{74} - 8 q^{75} + 344 q^{76} - 28 q^{77} - 16 q^{78} + 4 q^{79} + 24 q^{80} + 40 q^{81} + 68 q^{82} - 112 q^{83} + 48 q^{84} + 132 q^{85} - 24 q^{86} - 16 q^{87} + 72 q^{88} - 44 q^{90} - 26 q^{91} - 92 q^{92} - 96 q^{93} + 16 q^{94} - 102 q^{95} + 58 q^{96} - 84 q^{97} + 192 q^{98} + 8 q^{99} + O(q^{100}) \)

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.bg.a 525.bg 175.q $160$ $4.192$ None \(-2\) \(-20\) \(0\) \(4\) $\mathrm{SU}(2)[C_{15}]$
525.2.bg.b 525.bg 175.q $160$ $4.192$ None \(2\) \(20\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{15}]$

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

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