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Properties

Label 525.2.t
Level $525$
Weight $2$
Character orbit 525.t
Rep. character $\chi_{525}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $90$
Newform subspaces $10$
Sturm bound $160$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(13\), \(37\)

Dimensions

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

Total New Old
Modular forms 184 114 70
Cusp forms 136 90 46
Eisenstein series 48 24 24

Trace form

\( 90 q + 3 q^{3} + 42 q^{4} + 5 q^{7} - 3 q^{9} + O(q^{10}) \) \( 90 q + 3 q^{3} + 42 q^{4} + 5 q^{7} - 3 q^{9} + 24 q^{12} - 48 q^{16} + 2 q^{18} - 3 q^{19} - 6 q^{21} + 56 q^{22} + 36 q^{24} - 12 q^{28} + 15 q^{31} - 24 q^{33} - 12 q^{36} - 5 q^{37} - 3 q^{39} - 30 q^{42} - 26 q^{43} + 9 q^{49} + 18 q^{51} - 42 q^{52} - 90 q^{54} - 54 q^{57} + 32 q^{58} - 66 q^{61} + 19 q^{63} - 144 q^{64} - 72 q^{66} - 23 q^{67} + 10 q^{72} - 15 q^{73} + 48 q^{78} - 3 q^{79} + 21 q^{81} - 72 q^{82} + 36 q^{84} + 6 q^{87} + 16 q^{88} - 93 q^{91} - 27 q^{93} + 36 q^{94} + 162 q^{96} + 132 q^{99} + O(q^{100}) \)

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.t.a 525.t 21.g $2$ $4.192$ \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.2.t.b 525.t 21.g $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-3+\cdots)q^{7}+\cdots\)
525.2.t.c 525.t 21.g $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{7}+\cdots\)
525.2.t.d 525.t 21.g $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
525.2.t.e 525.t 21.g $2$ $4.192$ \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(0\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.t.f 525.t 21.g $8$ $4.192$ 8.0.856615824.2 None \(-3\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{3}-\beta _{7})q^{3}+\cdots\)
525.2.t.g 525.t 21.g $8$ $4.192$ 8.0.856615824.2 None \(3\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
525.2.t.h 525.t 21.g $20$ $4.192$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{4}+\beta _{11}+\cdots)q^{4}+\cdots\)
525.2.t.i 525.t 21.g $20$ $4.192$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+\beta _{4}q^{3}+(\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
525.2.t.j 525.t 21.g $24$ $4.192$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)