Properties

Label 725.6.a
Level $725$
Weight $6$
Character orbit 725.a
Rep. character $\chi_{725}(1,\cdot)$
Character field $\Q$
Dimension $221$
Newform subspaces $12$
Sturm bound $450$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 725.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(450\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(725))\).

Total New Old
Modular forms 380 221 159
Cusp forms 368 221 147
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(51\)
\(+\)\(-\)\(-\)\(54\)
\(-\)\(+\)\(-\)\(61\)
\(-\)\(-\)\(+\)\(55\)
Plus space\(+\)\(106\)
Minus space\(-\)\(115\)

Trace form

\( 221 q + 4 q^{2} - 6 q^{3} + 3484 q^{4} + 188 q^{6} + 212 q^{7} - 54 q^{8} + 17611 q^{9} + 290 q^{11} + 1562 q^{12} - 52 q^{13} - 780 q^{14} + 56492 q^{16} - 1454 q^{17} + 2154 q^{18} + 8108 q^{19} - 6916 q^{21}+ \cdots - 649576 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(725))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 29
725.6.a.a 725.a 1.a $4$ $116.278$ 4.4.3257317.1 None 29.6.a.a \(0\) \(28\) \(0\) \(208\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(7-\beta _{1}-\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
725.6.a.b 725.a 1.a $7$ $116.278$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 29.6.a.b \(-4\) \(-26\) \(0\) \(-184\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-4-\beta _{5})q^{3}+(23+\cdots)q^{4}+\cdots\)
725.6.a.c 725.a 1.a $11$ $116.278$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 145.6.a.b \(9\) \(-20\) \(0\) \(18\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(11+\beta _{2}+\cdots)q^{4}+\cdots\)
725.6.a.d 725.a 1.a $11$ $116.278$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 145.6.a.a \(15\) \(52\) \(0\) \(468\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(5-\beta _{4})q^{3}+(17+3\beta _{1}+\cdots)q^{4}+\cdots\)
725.6.a.e 725.a 1.a $13$ $116.278$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 145.6.a.d \(-9\) \(-38\) \(0\) \(-316\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-3+\beta _{5})q^{3}+(23+\cdots)q^{4}+\cdots\)
725.6.a.f 725.a 1.a $13$ $116.278$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 145.6.a.c \(-7\) \(-2\) \(0\) \(18\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2^{4}+\beta _{2}+\cdots)q^{4}+\cdots\)
725.6.a.g 725.a 1.a $23$ $116.278$ None 725.6.a.g \(-8\) \(-74\) \(0\) \(-494\) $-$ $-$ $\mathrm{SU}(2)$
725.6.a.h 725.a 1.a $23$ $116.278$ None 725.6.a.h \(0\) \(-34\) \(0\) \(-290\) $+$ $+$ $\mathrm{SU}(2)$
725.6.a.i 725.a 1.a $23$ $116.278$ None 725.6.a.h \(0\) \(34\) \(0\) \(290\) $-$ $+$ $\mathrm{SU}(2)$
725.6.a.j 725.a 1.a $23$ $116.278$ None 725.6.a.g \(8\) \(74\) \(0\) \(494\) $+$ $-$ $\mathrm{SU}(2)$
725.6.a.k 725.a 1.a $32$ $116.278$ None 145.6.b.a \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
725.6.a.l 725.a 1.a $38$ $116.278$ None 145.6.b.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(725))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(725)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)