Properties

Label 825.4.a
Level $825$
Weight $4$
Character orbit 825.a
Rep. character $\chi_{825}(1,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $30$
Sturm bound $480$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 825.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(480\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(825))\).

Total New Old
Modular forms 372 94 278
Cusp forms 348 94 254
Eisenstein series 24 0 24

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

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(-\)\(+\)\(14\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(52\)
Minus space\(-\)\(42\)

Trace form

\( 94q + 4q^{2} + 356q^{4} + 12q^{6} - 32q^{7} - 36q^{8} + 846q^{9} + O(q^{10}) \) \( 94q + 4q^{2} + 356q^{4} + 12q^{6} - 32q^{7} - 36q^{8} + 846q^{9} - 24q^{12} + 172q^{13} + 28q^{14} + 1388q^{16} - 24q^{17} + 36q^{18} + 32q^{19} - 36q^{21} + 44q^{22} - 108q^{23} + 324q^{24} + 1532q^{26} + 216q^{28} + 480q^{29} - 480q^{31} - 84q^{32} + 66q^{33} + 368q^{34} + 3204q^{36} - 236q^{37} + 592q^{38} - 504q^{39} + 560q^{41} - 468q^{42} + 584q^{43} + 616q^{44} - 296q^{46} + 172q^{47} + 240q^{48} + 4526q^{49} + 864q^{51} - 232q^{52} + 776q^{53} + 108q^{54} + 252q^{56} + 84q^{57} + 1248q^{58} + 40q^{59} - 5460q^{61} + 2096q^{62} - 288q^{63} + 7972q^{64} - 264q^{66} + 1344q^{67} + 136q^{68} - 1140q^{69} - 396q^{71} - 324q^{72} - 3740q^{73} - 5776q^{74} - 248q^{76} - 176q^{77} - 852q^{78} + 3824q^{79} + 7614q^{81} - 2040q^{82} + 1912q^{83} + 2400q^{84} - 2552q^{86} - 504q^{87} + 924q^{88} - 6700q^{89} - 3960q^{91} + 2460q^{92} - 1824q^{93} + 9576q^{94} + 10044q^{96} + 812q^{97} + 6316q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(825))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 11
825.4.a.a \(1\) \(48.677\) \(\Q\) None \(-5\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q-5q^{2}-3q^{3}+17q^{4}+15q^{6}-3q^{7}+\cdots\)
825.4.a.b \(1\) \(48.677\) \(\Q\) None \(-4\) \(3\) \(0\) \(21\) \(-\) \(+\) \(-\) \(q-4q^{2}+3q^{3}+8q^{4}-12q^{6}+21q^{7}+\cdots\)
825.4.a.c \(1\) \(48.677\) \(\Q\) None \(-3\) \(-3\) \(0\) \(-7\) \(+\) \(-\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}+9q^{6}-7q^{7}+\cdots\)
825.4.a.d \(1\) \(48.677\) \(\Q\) None \(-1\) \(-3\) \(0\) \(-36\) \(+\) \(+\) \(-\) \(q-q^{2}-3q^{3}-7q^{4}+3q^{6}-6^{2}q^{7}+\cdots\)
825.4.a.e \(1\) \(48.677\) \(\Q\) None \(0\) \(3\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+3q^{3}-8q^{4}-2q^{7}+9q^{9}-11q^{11}+\cdots\)
825.4.a.f \(1\) \(48.677\) \(\Q\) None \(1\) \(3\) \(0\) \(26\) \(-\) \(+\) \(-\) \(q+q^{2}+3q^{3}-7q^{4}+3q^{6}+26q^{7}+\cdots\)
825.4.a.g \(1\) \(48.677\) \(\Q\) None \(3\) \(3\) \(0\) \(7\) \(-\) \(+\) \(-\) \(q+3q^{2}+3q^{3}+q^{4}+9q^{6}+7q^{7}+\cdots\)
825.4.a.h \(1\) \(48.677\) \(\Q\) None \(4\) \(-3\) \(0\) \(-21\) \(+\) \(-\) \(-\) \(q+4q^{2}-3q^{3}+8q^{4}-12q^{6}-21q^{7}+\cdots\)
825.4.a.i \(1\) \(48.677\) \(\Q\) None \(5\) \(-3\) \(0\) \(32\) \(+\) \(+\) \(+\) \(q+5q^{2}-3q^{3}+17q^{4}-15q^{6}+2^{5}q^{7}+\cdots\)
825.4.a.j \(1\) \(48.677\) \(\Q\) None \(5\) \(3\) \(0\) \(3\) \(-\) \(-\) \(+\) \(q+5q^{2}+3q^{3}+17q^{4}+15q^{6}+3q^{7}+\cdots\)
825.4.a.k \(2\) \(48.677\) \(\Q(\sqrt{33}) \) None \(-1\) \(-6\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-\beta q^{2}-3q^{3}+\beta q^{4}+3\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
825.4.a.l \(2\) \(48.677\) \(\Q(\sqrt{97}) \) None \(-1\) \(6\) \(0\) \(-24\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+3q^{3}+(2^{4}+\beta )q^{4}-3\beta q^{6}+\cdots\)
825.4.a.m \(2\) \(48.677\) \(\Q(\sqrt{17}) \) None \(1\) \(-6\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-3q^{3}+(-4+\beta )q^{4}-3\beta q^{6}+\cdots\)
825.4.a.n \(3\) \(48.677\) 3.3.788.1 None \(-1\) \(9\) \(0\) \(16\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{2}+3q^{3}+(-2-\beta _{1})q^{4}-3\beta _{2}q^{6}+\cdots\)
825.4.a.o \(3\) \(48.677\) 3.3.3368.1 None \(-1\) \(9\) \(0\) \(-16\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(3+2\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
825.4.a.p \(3\) \(48.677\) 3.3.1957.1 None \(-1\) \(9\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{1}+2\beta _{2})q^{4}+\cdots\)
825.4.a.q \(3\) \(48.677\) 3.3.3368.1 None \(1\) \(-9\) \(0\) \(16\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(3+2\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
825.4.a.r \(3\) \(48.677\) 3.3.47528.1 None \(2\) \(-9\) \(0\) \(-10\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-3q^{3}+(10+\beta _{2})q^{4}+\cdots\)
825.4.a.s \(3\) \(48.677\) 3.3.23612.1 None \(4\) \(9\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}+3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
825.4.a.t \(4\) \(48.677\) 4.4.1540841.1 None \(-4\) \(-12\) \(0\) \(-34\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}-3q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
825.4.a.u \(4\) \(48.677\) 4.4.91035289.2 None \(-2\) \(12\) \(0\) \(-11\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}+3q^{3}+(-4-\beta _{3})q^{4}+3\beta _{3}q^{6}+\cdots\)
825.4.a.v \(4\) \(48.677\) 4.4.91035289.2 None \(2\) \(-12\) \(0\) \(11\) \(+\) \(+\) \(+\) \(q-\beta _{3}q^{2}-3q^{3}+(-4-\beta _{3})q^{4}+3\beta _{3}q^{6}+\cdots\)
825.4.a.w \(5\) \(48.677\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4\) \(-15\) \(0\) \(38\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-3q^{3}+(9-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
825.4.a.x \(5\) \(48.677\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(15\) \(0\) \(-18\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+3q^{3}+(1+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
825.4.a.y \(5\) \(48.677\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(-15\) \(0\) \(18\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
825.4.a.z \(5\) \(48.677\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4\) \(15\) \(0\) \(-38\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(9-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
825.4.a.ba \(7\) \(48.677\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(21\) \(0\) \(-34\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+3q^{3}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
825.4.a.bb \(7\) \(48.677\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-21\) \(0\) \(-50\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
825.4.a.bc \(7\) \(48.677\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(21\) \(0\) \(50\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
825.4.a.bd \(7\) \(48.677\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(5\) \(-21\) \(0\) \(34\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}-3q^{3}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(825))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(825)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)