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Properties

Label 525.2.n
Level $525$
Weight $2$
Character orbit 525.n
Rep. character $\chi_{525}(106,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $112$
Newform subspaces $5$
Sturm bound $160$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 336 112 224
Cusp forms 304 112 192
Eisenstein series 32 0 32

Trace form

\( 112 q + 4 q^{2} - 24 q^{4} + 8 q^{5} + 12 q^{8} - 28 q^{9} + O(q^{10}) \) \( 112 q + 4 q^{2} - 24 q^{4} + 8 q^{5} + 12 q^{8} - 28 q^{9} + 12 q^{10} + 16 q^{12} + 24 q^{13} + 4 q^{15} - 40 q^{16} + 32 q^{17} - 16 q^{18} - 12 q^{19} - 60 q^{20} + 4 q^{21} - 56 q^{22} - 12 q^{23} + 8 q^{25} + 64 q^{26} + 20 q^{29} - 8 q^{30} - 72 q^{32} - 12 q^{33} - 36 q^{34} + 4 q^{35} - 24 q^{36} - 16 q^{37} + 56 q^{38} + 16 q^{39} - 96 q^{40} + 48 q^{41} + 48 q^{43} - 84 q^{44} + 8 q^{45} + 4 q^{46} - 48 q^{47} + 32 q^{48} + 112 q^{49} - 72 q^{50} - 64 q^{51} + 88 q^{52} - 12 q^{53} - 68 q^{55} + 24 q^{57} - 112 q^{58} + 24 q^{59} + 28 q^{60} + 8 q^{61} - 28 q^{62} - 24 q^{64} - 88 q^{65} + 16 q^{66} + 24 q^{67} + 128 q^{68} + 8 q^{69} + 16 q^{70} - 32 q^{71} + 12 q^{72} + 64 q^{73} + 24 q^{74} + 32 q^{75} + 72 q^{76} - 24 q^{77} + 24 q^{78} + 24 q^{79} + 152 q^{80} - 28 q^{81} + 56 q^{82} + 68 q^{83} + 12 q^{84} - 8 q^{85} - 120 q^{86} - 48 q^{87} + 36 q^{88} - 96 q^{89} + 12 q^{90} + 16 q^{91} - 48 q^{92} - 80 q^{93} + 52 q^{94} - 180 q^{95} + 20 q^{96} + 12 q^{97} + 4 q^{98} + O(q^{100}) \)

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.n.a 525.n 25.d $4$ $4.192$ \(\Q(\zeta_{10})\) None \(3\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
525.2.n.b 525.n 25.d $20$ $4.192$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(5\) \(5\) \(-20\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{10}q^{2}+\beta _{4}q^{3}+(\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
525.2.n.c 525.n 25.d $24$ $4.192$ None \(1\) \(-6\) \(-1\) \(24\) $\mathrm{SU}(2)[C_{5}]$
525.2.n.d 525.n 25.d $32$ $4.192$ None \(1\) \(-8\) \(-3\) \(-32\) $\mathrm{SU}(2)[C_{5}]$
525.2.n.e 525.n 25.d $32$ $4.192$ None \(1\) \(8\) \(7\) \(32\) $\mathrm{SU}(2)[C_{5}]$

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

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