Properties

Label 525.3.s
Level $525$
Weight $3$
Character orbit 525.s
Rep. character $\chi_{525}(124,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $10$
Sturm bound $240$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(240\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

Total New Old
Modular forms 344 96 248
Cusp forms 296 96 200
Eisenstein series 48 0 48

Trace form

\( 96 q + 96 q^{4} - 144 q^{9} + O(q^{10}) \) \( 96 q + 96 q^{4} - 144 q^{9} + 36 q^{11} - 60 q^{14} - 240 q^{16} + 150 q^{19} + 6 q^{21} + 192 q^{26} + 96 q^{29} - 48 q^{31} - 576 q^{36} + 18 q^{39} - 420 q^{44} + 120 q^{46} - 462 q^{49} - 24 q^{51} + 516 q^{56} + 1128 q^{59} - 102 q^{61} - 1440 q^{64} + 216 q^{66} - 528 q^{71} - 600 q^{74} + 120 q^{79} - 432 q^{81} - 600 q^{84} + 252 q^{86} - 48 q^{89} + 678 q^{91} + 1368 q^{94} - 900 q^{96} - 216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.3.s.a $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.b $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.c $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.d $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{6}+\cdots\)
525.3.s.e $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.f $4$ $14.305$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.g $8$ $14.305$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots\)
525.3.s.h $16$ $14.305$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}+(-\beta _{10}+2\beta _{13})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.3.s.i $24$ $14.305$ None \(0\) \(0\) \(0\) \(0\)
525.3.s.j $24$ $14.305$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)