Properties

Label 825.2.n
Level $825$
Weight $2$
Character orbit 825.n
Rep. character $\chi_{825}(301,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $152$
Newform subspaces $16$
Sturm bound $240$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 16 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

Total New Old
Modular forms 528 152 376
Cusp forms 432 152 280
Eisenstein series 96 0 96

Trace form

\( 152 q - 4 q^{2} - 42 q^{4} + 2 q^{6} - 6 q^{7} + 8 q^{8} - 38 q^{9} + 10 q^{11} + 8 q^{12} + 6 q^{13} - 6 q^{14} - 34 q^{16} + 2 q^{17} + 6 q^{18} + 20 q^{19} - 16 q^{21} + 36 q^{22} + 20 q^{23} + 24 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.2.n.a 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 825.2.n.a \(-3\) \(-1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.b 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 825.2.n.b \(-2\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.c 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 33.2.e.b \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
825.2.n.d 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 825.2.n.b \(2\) \(-1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.e 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 825.2.n.a \(3\) \(1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.f 825.n 11.c $4$ $6.588$ \(\Q(\zeta_{10})\) None 33.2.e.a \(3\) \(1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.g 825.n 11.c $8$ $6.588$ 8.0.13140625.1 None 165.2.m.d \(-4\) \(2\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
825.2.n.h 825.n 11.c $8$ $6.588$ 8.0.819390625.1 None 825.2.n.h \(-3\) \(2\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.i 825.n 11.c $8$ $6.588$ 8.0.819390625.1 None 165.2.m.b \(-2\) \(-2\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
825.2.n.j 825.n 11.c $8$ $6.588$ \(\Q(\zeta_{15})\) None 165.2.m.c \(-2\) \(-2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
825.2.n.k 825.n 11.c $8$ $6.588$ 8.0.13140625.1 None 165.2.m.a \(0\) \(2\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(1+\cdots)q^{3}+\cdots\)
825.2.n.l 825.n 11.c $8$ $6.588$ 8.0.819390625.1 None 825.2.n.h \(3\) \(-2\) \(0\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{6})q^{3}+\cdots\)
825.2.n.m 825.n 11.c $16$ $6.588$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 825.2.n.m \(-2\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{6})q^{2}-\beta _{11}q^{3}+\cdots\)
825.2.n.n 825.n 11.c $16$ $6.588$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 825.2.n.m \(2\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{6})q^{2}+\beta _{11}q^{3}+\cdots\)
825.2.n.o 825.n 11.c $24$ $6.588$ None 165.2.s.a \(-2\) \(6\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$
825.2.n.p 825.n 11.c $24$ $6.588$ None 165.2.s.a \(2\) \(-6\) \(0\) \(4\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)