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 $14$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
825.4.c.a \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+5iq^{2}+3iq^{3}-17q^{4}-15q^{6}+\cdots\)
825.4.c.b \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+5iq^{2}-3iq^{3}-17q^{4}+15q^{6}+\cdots\)
825.4.c.c \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{2}+3iq^{3}-8q^{4}-12q^{6}-21iq^{7}+\cdots\)
825.4.c.d \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{2}-3iq^{3}-q^{4}+9q^{6}+7iq^{7}+\cdots\)
825.4.c.e \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}+6^{2}iq^{7}+\cdots\)
825.4.c.f \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}+26iq^{7}+\cdots\)
825.4.c.g \(2\) \(48.677\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-3iq^{3}+8q^{4}-2iq^{7}-9q^{9}-11q^{11}+\cdots\)
825.4.c.h \(4\) \(48.677\) \(\Q(i, \sqrt{97})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(-17+\beta _{3})q^{4}+\cdots\)
825.4.c.i \(4\) \(48.677\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)
825.4.c.j \(4\) \(48.677\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-3+\cdots)q^{6}+\cdots\)
825.4.c.k \(6\) \(48.677\) 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(-10+\beta _{4}+\cdots)q^{4}+\cdots\)
825.4.c.l \(6\) \(48.677\) 6.0.2230106176.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.m \(6\) \(48.677\) 6.0.245110336.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+3\beta _{1}q^{3}+(-6-2\beta _{3}+\beta _{5})q^{4}+\cdots\)
825.4.c.n \(6\) \(48.677\) 6.0.181494784.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-3\beta _{4}q^{3}+(-3+2\beta _{2})q^{4}+\cdots\)
825.4.c.o \(6\) \(48.677\) 6.0.9935104.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+3\beta _{3}q^{3}+(2-\beta _{4})q^{4}+3\beta _{1}q^{6}+\cdots\)
825.4.c.p \(8\) \(48.677\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-7+\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.q \(8\) \(48.677\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{2}+3\beta _{3}q^{3}+(3+\beta _{1})q^{4}+\cdots\)
825.4.c.r \(10\) \(48.677\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-9-\beta _{3}+\cdots)q^{4}+\cdots\)
825.4.c.s \(10\) \(48.677\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+\cdots\)

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

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