Properties

Label 525.2.b
Level $525$
Weight $2$
Character orbit 525.b
Rep. character $\chi_{525}(251,\cdot)$
Character field $\Q$
Dimension $44$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(11\), \(17\), \(37\)

Dimensions

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

Total New Old
Modular forms 92 56 36
Cusp forms 68 44 24
Eisenstein series 24 12 12

Trace form

\( 44 q - 32 q^{4} + 8 q^{7} + O(q^{10}) \) \( 44 q - 32 q^{4} + 8 q^{7} + 8 q^{16} + 4 q^{18} - 18 q^{21} - 8 q^{22} - 16 q^{28} + 16 q^{37} - 36 q^{42} + 40 q^{43} - 24 q^{46} - 34 q^{49} + 12 q^{51} + 12 q^{57} - 8 q^{58} + 44 q^{63} + 64 q^{64} - 24 q^{67} - 64 q^{72} - 84 q^{78} - 104 q^{79} + 108 q^{84} - 16 q^{88} + 6 q^{91} - 12 q^{93} - 36 q^{99} + O(q^{100}) \)

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.b.a 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.b 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.c 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.b.d 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(3-\zeta_{6})q^{7}+\cdots\)
525.2.b.e 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.f 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{3}+2q^{4}+(\beta _{1}-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
525.2.b.g 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.h 525.b 21.c $8$ $4.192$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2+\beta _{4})q^{4}+\beta _{3}q^{6}+\cdots\)
525.2.b.i 525.b 21.c $8$ $4.192$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-2+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots\)
525.2.b.j 525.b 21.c $8$ $4.192$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}-q^{4}+(\zeta_{24}^{2}+\cdots)q^{6}+\cdots\)

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

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