Properties

Label 825.4.c
Level $825$
Weight $4$
Character orbit 825.c
Rep. character $\chi_{825}(199,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $19$
Sturm bound $480$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(480\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(825, [\chi])\).

Total New Old
Modular forms 372 92 280
Cusp forms 348 92 256
Eisenstein series 24 0 24

Trace form

\( 92 q - 360 q^{4} + 24 q^{6} - 828 q^{9} + 472 q^{14} + 1624 q^{16} - 24 q^{19} + 48 q^{21} - 648 q^{24} + 512 q^{26} + 976 q^{29} + 848 q^{31} - 1712 q^{34} + 3240 q^{36} + 168 q^{39} - 1984 q^{41} - 1232 q^{44}+ \cdots + 2808 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
825.4.c.a 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 33.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5 i q^{2}+3 i q^{3}-17 q^{4}-15 q^{6}+\cdots\)
825.4.c.b 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 825.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5 i q^{2}-3 i q^{3}-17 q^{4}+15 q^{6}+\cdots\)
825.4.c.c 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 825.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4 i q^{2}+3 i q^{3}-8 q^{4}-12 q^{6}+\cdots\)
825.4.c.d 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 825.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{2}-3 i q^{3}-q^{4}+9 q^{6}+7 i q^{7}+\cdots\)
825.4.c.e 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 165.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-3 i q^{3}+7 q^{4}+3 q^{6}+36 i q^{7}+\cdots\)
825.4.c.f 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 33.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-3 i q^{3}+7 q^{4}+3 q^{6}+26 i q^{7}+\cdots\)
825.4.c.g 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None 165.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}+8 q^{4}-2 i q^{7}-9 q^{9}+\cdots\)
825.4.c.h 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{97})\) None 33.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(-17+\beta _{3})q^{4}+\cdots\)
825.4.c.i 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{33})\) None 33.4.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)
825.4.c.j 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{17})\) None 165.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-3+\cdots)q^{6}+\cdots\)
825.4.c.k 825.c 5.b $6$ $48.677$ 6.0.\(\cdots\).1 None 165.4.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(-10+\beta _{4}+\cdots)q^{4}+\cdots\)
825.4.c.l 825.c 5.b $6$ $48.677$ 6.0.2230106176.1 None 165.4.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.m 825.c 5.b $6$ $48.677$ 6.0.245110336.2 None 165.4.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+3\beta _{1}q^{3}+(-6-2\beta _{3}+\beta _{5})q^{4}+\cdots\)
825.4.c.n 825.c 5.b $6$ $48.677$ 6.0.181494784.1 None 825.4.a.o \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-3\beta _{4}q^{3}+(-3+2\beta _{2})q^{4}+\cdots\)
825.4.c.o 825.c 5.b $6$ $48.677$ 6.0.9935104.1 None 165.4.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+3\beta _{3}q^{3}+(2-\beta _{4})q^{4}+3\beta _{1}q^{6}+\cdots\)
825.4.c.p 825.c 5.b $8$ $48.677$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 165.4.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.q 825.c 5.b $8$ $48.677$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 825.4.a.u \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(3+\beta _{1})q^{4}+\cdots\)
825.4.c.r 825.c 5.b $10$ $48.677$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 825.4.a.w \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-9-\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.s 825.c 5.b $10$ $48.677$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 825.4.a.x \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)