Properties

Label 525.2.r
Level $525$
Weight $2$
Character orbit 525.r
Rep. character $\chi_{525}(424,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $8$
Sturm bound $160$
Trace bound $6$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(160\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

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

Total New Old
Modular forms 184 48 136
Cusp forms 136 48 88
Eisenstein series 48 0 48

Trace form

\( 48q + 24q^{4} + 8q^{6} + 24q^{9} + O(q^{10}) \) \( 48q + 24q^{4} + 8q^{6} + 24q^{9} - 4q^{11} + 36q^{14} - 40q^{16} + 22q^{19} - 2q^{21} + 12q^{24} + 24q^{26} - 32q^{29} - 32q^{31} - 32q^{34} + 48q^{36} - 2q^{39} - 8q^{41} + 36q^{44} - 8q^{46} + 74q^{49} - 8q^{51} + 4q^{54} - 108q^{56} + 8q^{59} - 2q^{61} - 208q^{64} - 40q^{66} - 48q^{69} + 80q^{71} - 8q^{74} - 8q^{76} - 12q^{79} - 24q^{81} - 72q^{84} + 12q^{86} - 32q^{89} + 58q^{91} + 48q^{94} - 8q^{96} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.2.r.a \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(-6\) \(0\) \(0\) \(10\) \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
525.2.r.b \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.r.c \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.d \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.e \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.f \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(6\) \(0\) \(0\) \(-10\) \(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+\cdots\)
525.2.r.g \(8\) \(4.192\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{7}q^{6}+(\zeta_{24}+\cdots)q^{7}+\cdots\)
525.2.r.h \(16\) \(4.192\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)

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

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