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

\( 92 q - 360 q^{4} + 24 q^{6} - 828 q^{9} + O(q^{10}) \) \( 92 q - 360 q^{4} + 24 q^{6} - 828 q^{9} + 472 q^{14} + 1624 q^{16} - 24 q^{19} + 48 q^{21} - 648 q^{24} + 512 q^{26} + 976 q^{29} + 848 q^{31} - 1712 q^{34} + 3240 q^{36} + 168 q^{39} - 1984 q^{41} - 1232 q^{44} + 1848 q^{46} - 5516 q^{49} + 1488 q^{51} - 216 q^{54} + 264 q^{56} + 2624 q^{59} - 5216 q^{61} - 4888 q^{64} + 528 q^{66} - 48 q^{69} - 1152 q^{71} + 9904 q^{74} + 152 q^{76} - 1024 q^{79} + 7452 q^{81} + 3744 q^{84} + 2616 q^{86} + 4768 q^{89} + 3064 q^{91} - 4088 q^{94} + 2808 q^{96} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM 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 \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5iq^{2}+3iq^{3}-17q^{4}-15q^{6}+\cdots\)
825.4.c.b 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5iq^{2}-3iq^{3}-17q^{4}+15q^{6}+\cdots\)
825.4.c.c 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{2}+3iq^{3}-8q^{4}-12q^{6}-21iq^{7}+\cdots\)
825.4.c.d 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{2}-3iq^{3}-q^{4}+9q^{6}+7iq^{7}+\cdots\)
825.4.c.e 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}+6^{2}iq^{7}+\cdots\)
825.4.c.f 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}+26iq^{7}+\cdots\)
825.4.c.g 825.c 5.b $2$ $48.677$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+8q^{4}-2iq^{7}-9q^{9}-11q^{11}+\cdots\)
825.4.c.h 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{97})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(-17+\beta _{3})q^{4}+\cdots\)
825.4.c.i 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)
825.4.c.j 825.c 5.b $4$ $48.677$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-3+\cdots)q^{6}+\cdots\)
825.4.c.k 825.c 5.b $6$ $48.677$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(-10+\beta _{4}+\cdots)q^{4}+\cdots\)
825.4.c.l 825.c 5.b $6$ $48.677$ 6.0.2230106176.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.m 825.c 5.b $6$ $48.677$ 6.0.245110336.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+3\beta _{1}q^{3}+(-6-2\beta _{3}+\beta _{5})q^{4}+\cdots\)
825.4.c.n 825.c 5.b $6$ $48.677$ 6.0.181494784.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-3\beta _{4}q^{3}+(-3+2\beta _{2})q^{4}+\cdots\)
825.4.c.o 825.c 5.b $6$ $48.677$ 6.0.9935104.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+3\beta _{3}q^{3}+(2-\beta _{4})q^{4}+3\beta _{1}q^{6}+\cdots\)
825.4.c.p 825.c 5.b $8$ $48.677$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.q 825.c 5.b $8$ $48.677$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(3+\beta _{1})q^{4}+\cdots\)
825.4.c.r 825.c 5.b $10$ $48.677$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-9-\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.s 825.c 5.b $10$ $48.677$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)

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

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