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Properties

Label 525.3.o
Level $525$
Weight $3$
Character orbit 525.o
Rep. character $\chi_{525}(376,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $102$
Newform subspaces $17$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 17 \)
Sturm bound: \(240\)
Trace bound: \(11\)
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 344 102 242
Cusp forms 296 102 194
Eisenstein series 48 0 48

Trace form

\( 102 q - 2 q^{2} - 3 q^{3} - 98 q^{4} - 5 q^{7} - 16 q^{8} + 153 q^{9} + O(q^{10}) \) \( 102 q - 2 q^{2} - 3 q^{3} - 98 q^{4} - 5 q^{7} - 16 q^{8} + 153 q^{9} - 18 q^{11} + 24 q^{12} - 38 q^{14} - 218 q^{16} + 48 q^{17} + 6 q^{18} - 117 q^{19} - 30 q^{21} - 68 q^{22} + 4 q^{23} - 54 q^{24} + 66 q^{26} + 282 q^{28} + 128 q^{29} + 123 q^{31} + 60 q^{32} - 108 q^{33} - 588 q^{36} + 71 q^{37} - 414 q^{38} - 9 q^{39} - 156 q^{42} - 94 q^{43} - 8 q^{44} - 188 q^{46} + 198 q^{47} + 155 q^{49} + 12 q^{51} + 408 q^{52} + 184 q^{53} - 292 q^{56} + 102 q^{57} + 58 q^{58} - 84 q^{59} + 474 q^{61} + 69 q^{63} + 1172 q^{64} + 108 q^{66} - 235 q^{67} + 168 q^{68} + 36 q^{71} - 24 q^{72} - 453 q^{73} - 442 q^{74} - 8 q^{77} - 36 q^{78} + 19 q^{79} - 459 q^{81} - 540 q^{82} - 240 q^{84} - 70 q^{86} - 54 q^{87} + 746 q^{88} - 12 q^{89} - 179 q^{91} - 189 q^{93} - 456 q^{94} + 666 q^{96} + 352 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.3.o.a 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
525.3.o.b 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(0\) \(7\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{6}+\cdots\)
525.3.o.c 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
525.3.o.d 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(11\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
525.3.o.e 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(-11\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
525.3.o.f 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(7\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
525.3.o.g 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(7\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
525.3.o.h 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(0\) \(-13\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
525.3.o.i 525.o 7.d $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(0\) \(7\) $\mathrm{SU}(2)[C_{6}]$ \(q+3\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
525.3.o.j 525.o 7.d $4$ $14.305$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(6\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(-3+\cdots)q^{4}+\cdots\)
525.3.o.k 525.o 7.d $4$ $14.305$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(-6\) \(0\) \(26\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(-3+\cdots)q^{4}+\cdots\)
525.3.o.l 525.o 7.d $8$ $14.305$ 8.0.\(\cdots\).16 None \(-2\) \(12\) \(0\) \(16\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
525.3.o.m 525.o 7.d $12$ $14.305$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-18\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(-2-\beta _{5})q^{3}+(4\beta _{5}+\beta _{11})q^{4}+\cdots\)
525.3.o.n 525.o 7.d $12$ $14.305$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-18\) \(0\) \(7\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{2})q^{3}+(-2+\cdots)q^{4}+\cdots\)
525.3.o.o 525.o 7.d $12$ $14.305$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(18\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{6})q^{2}+(1-\beta _{2})q^{3}+(-2+\cdots)q^{4}+\cdots\)
525.3.o.p 525.o 7.d $16$ $14.305$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-24\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
525.3.o.q 525.o 7.d $16$ $14.305$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(24\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(2+\beta _{4})q^{3}+(2\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)