↑

Properties

Label 525.2.z
Level $525$
Weight $2$
Character orbit 525.z
Rep. character $\chi_{525}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $128$
Newform subspaces $2$
Sturm bound $160$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 336 128 208
Cusp forms 304 128 176
Eisenstein series 32 0 32

Trace form

\( 128 q + 36 q^{4} - 4 q^{5} + 32 q^{9} + O(q^{10}) \) \( 128 q + 36 q^{4} - 4 q^{5} + 32 q^{9} + 8 q^{10} - 4 q^{15} - 20 q^{16} - 12 q^{19} - 12 q^{20} - 4 q^{21} + 80 q^{22} - 20 q^{23} + 28 q^{25} - 24 q^{26} - 20 q^{29} - 8 q^{30} - 20 q^{33} + 24 q^{34} - 4 q^{35} - 36 q^{36} + 20 q^{37} + 16 q^{39} - 36 q^{40} - 8 q^{41} - 84 q^{44} + 4 q^{45} - 4 q^{46} - 80 q^{47} - 128 q^{49} + 148 q^{50} + 64 q^{51} + 40 q^{53} - 12 q^{55} - 80 q^{58} + 24 q^{59} + 4 q^{60} + 32 q^{61} - 100 q^{62} + 36 q^{64} + 116 q^{65} - 16 q^{66} - 40 q^{67} + 8 q^{69} - 8 q^{70} + 32 q^{71} - 40 q^{73} - 16 q^{74} - 16 q^{75} - 72 q^{76} + 40 q^{77} + 24 q^{79} - 44 q^{80} - 32 q^{81} + 60 q^{83} + 12 q^{84} - 76 q^{85} + 120 q^{86} - 80 q^{87} - 140 q^{88} - 36 q^{89} - 8 q^{90} - 16 q^{91} - 200 q^{92} + 12 q^{94} + 124 q^{95} + 20 q^{96} + 60 q^{97} + O(q^{100}) \)

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.z.a 525.z 25.e $56$ $4.192$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{10}]$
525.2.z.b 525.z 25.e $72$ $4.192$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)