Properties

Label 525.3.h
Level $525$
Weight $3$
Character orbit 525.h
Rep. character $\chi_{525}(76,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $5$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 172 50 122
Cusp forms 148 50 98
Eisenstein series 24 0 24

Trace form

\( 50 q + 2 q^{2} + 90 q^{4} + 6 q^{7} + 10 q^{8} - 150 q^{9} + O(q^{10}) \) \( 50 q + 2 q^{2} + 90 q^{4} + 6 q^{7} + 10 q^{8} - 150 q^{9} + 12 q^{11} + 14 q^{14} + 106 q^{16} - 6 q^{18} - 30 q^{21} + 68 q^{22} + 92 q^{23} - 82 q^{28} - 20 q^{29} + 162 q^{32} - 270 q^{36} - 84 q^{37} - 60 q^{39} + 84 q^{42} - 204 q^{43} + 176 q^{44} - 376 q^{46} + 132 q^{49} - 48 q^{51} - 196 q^{53} + 358 q^{56} + 168 q^{57} + 476 q^{58} - 18 q^{63} + 662 q^{64} - 316 q^{67} + 228 q^{71} - 30 q^{72} + 256 q^{74} - 28 q^{77} - 432 q^{78} - 84 q^{79} + 450 q^{81} - 432 q^{84} - 1256 q^{86} + 676 q^{88} + 350 q^{91} - 276 q^{92} + 48 q^{93} - 790 q^{98} - 36 q^{99} + O(q^{100}) \)

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.h.a 525.h 7.b $2$ $14.305$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\zeta_{6}q^{3}-3q^{4}-\zeta_{6}q^{6}+(-1+\cdots)q^{7}+\cdots\)
525.3.h.b 525.h 7.b $10$ $14.305$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots\)
525.3.h.c 525.h 7.b $10$ $14.305$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{1}-\beta _{3})q^{4}+\cdots\)
525.3.h.d 525.h 7.b $12$ $14.305$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{3}q^{3}+(4+\beta _{1})q^{4}-\beta _{9}q^{6}+\cdots\)
525.3.h.e 525.h 7.b $16$ $14.305$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(2+\beta _{1})q^{4}+\beta _{4}q^{6}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)