Properties

Label 882.4.a
Level $882$
Weight $4$
Character orbit 882.a
Rep. character $\chi_{882}(1,\cdot)$
Character field $\Q$
Dimension $51$
Newform subspaces $35$
Sturm bound $672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(672\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(882))\).

Total New Old
Modular forms 536 51 485
Cusp forms 472 51 421
Eisenstein series 64 0 64

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(27\)
Minus space\(-\)\(24\)

Trace form

\( 51q + 2q^{2} + 204q^{4} + 8q^{8} + O(q^{10}) \) \( 51q + 2q^{2} + 204q^{4} + 8q^{8} + 32q^{10} - 56q^{11} + 68q^{13} + 816q^{16} - 162q^{17} - 198q^{19} - 56q^{22} - 28q^{23} + 909q^{25} - 152q^{26} + 530q^{29} + 692q^{31} + 32q^{32} + 148q^{34} + 1170q^{37} - 260q^{38} + 128q^{40} + 798q^{41} + 4q^{43} - 224q^{44} - 32q^{46} - 180q^{47} - 314q^{50} + 272q^{52} - 182q^{53} - 80q^{55} + 396q^{58} - 1986q^{59} + 1112q^{61} + 472q^{62} + 3264q^{64} - 792q^{65} + 816q^{67} - 648q^{68} + 2568q^{71} + 1342q^{73} + 1956q^{74} - 792q^{76} - 956q^{79} + 1236q^{82} + 78q^{83} - 1436q^{85} + 616q^{86} - 224q^{88} + 1650q^{89} - 112q^{92} - 792q^{94} - 764q^{95} - 902q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(882))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
882.4.a.a \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(-22\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}+4q^{4}-22q^{5}-8q^{8}+44q^{10}+\cdots\)
882.4.a.b \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(-12\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}-12q^{5}-8q^{8}+24q^{10}+\cdots\)
882.4.a.c \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(-9\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}-9q^{5}-8q^{8}+18q^{10}+\cdots\)
882.4.a.d \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}+2q^{5}-8q^{8}-4q^{10}+\cdots\)
882.4.a.e \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(6\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}+4q^{4}+6q^{5}-8q^{8}-12q^{10}+\cdots\)
882.4.a.f \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(9\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+4q^{4}+9q^{5}-8q^{8}-18q^{10}+\cdots\)
882.4.a.g \(1\) \(52.040\) \(\Q\) None \(-2\) \(0\) \(18\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}+18q^{5}-8q^{8}-6^{2}q^{10}+\cdots\)
882.4.a.h \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-15\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-15q^{5}+8q^{8}-30q^{10}+\cdots\)
882.4.a.i \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-14\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-14q^{5}+8q^{8}-28q^{10}+\cdots\)
882.4.a.j \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-8\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots\)
882.4.a.k \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-7\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}-7q^{5}+8q^{8}-14q^{10}+\cdots\)
882.4.a.l \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-6\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\cdots\)
882.4.a.m \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\cdots\)
882.4.a.n \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(6\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\cdots\)
882.4.a.o \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(6\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\cdots\)
882.4.a.p \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(7\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}+7q^{5}+8q^{8}+14q^{10}+\cdots\)
882.4.a.q \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(8\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+4q^{4}+8q^{5}+8q^{8}+2^{4}q^{10}+\cdots\)
882.4.a.r \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(15\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}+15q^{5}+8q^{8}+30q^{10}+\cdots\)
882.4.a.s \(1\) \(52.040\) \(\Q\) None \(2\) \(0\) \(22\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}+4q^{4}+22q^{5}+8q^{8}+44q^{10}+\cdots\)
882.4.a.t \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(-12\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+4q^{4}+(-6+\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.u \(2\) \(52.040\) \(\Q(\sqrt{193}) \) None \(-4\) \(0\) \(-7\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}+4q^{4}+(-3-\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.v \(2\) \(52.040\) \(\Q(\sqrt{1345}) \) None \(-4\) \(0\) \(-5\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+4q^{4}+(-2-\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.w \(2\) \(52.040\) \(\Q(\sqrt{22}) \) None \(-4\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}-2\beta q^{10}+\cdots\)
882.4.a.x \(2\) \(52.040\) \(\Q(\sqrt{58}) \) None \(-4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}-2\beta q^{10}+\cdots\)
882.4.a.y \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{2}+4q^{4}+5\beta q^{5}-8q^{8}-10\beta q^{10}+\cdots\)
882.4.a.z \(2\) \(52.040\) \(\Q(\sqrt{1345}) \) None \(-4\) \(0\) \(5\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+4q^{4}+(3-\beta )q^{5}-8q^{8}+(-6+\cdots)q^{10}+\cdots\)
882.4.a.ba \(2\) \(52.040\) \(\Q(\sqrt{193}) \) None \(-4\) \(0\) \(7\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{2}+4q^{4}+(4-\beta )q^{5}-8q^{8}+(-8+\cdots)q^{10}+\cdots\)
882.4.a.bb \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(12\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+4q^{4}+(6+\beta )q^{5}-8q^{8}+(-12+\cdots)q^{10}+\cdots\)
882.4.a.bc \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(-12\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}+(-6+\beta )q^{5}+8q^{8}+\cdots\)
882.4.a.bd \(2\) \(52.040\) \(\Q(\sqrt{193}) \) None \(4\) \(0\) \(-7\) \(0\) \(-\) \(+\) \(+\) \(q+2q^{2}+4q^{4}+(-3-\beta )q^{5}+8q^{8}+\cdots\)
882.4.a.be \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+2q^{2}+4q^{4}+5\beta q^{5}+8q^{8}+10\beta q^{10}+\cdots\)
882.4.a.bf \(2\) \(52.040\) \(\Q(\sqrt{58}) \) None \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+2\beta q^{10}+\cdots\)
882.4.a.bg \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}+14\beta q^{5}+8q^{8}+28\beta q^{10}+\cdots\)
882.4.a.bh \(2\) \(52.040\) \(\Q(\sqrt{193}) \) None \(4\) \(0\) \(7\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}+4q^{4}+(4-\beta )q^{5}+8q^{8}+(8+\cdots)q^{10}+\cdots\)
882.4.a.bi \(2\) \(52.040\) \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(12\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+4q^{4}+(6+\beta )q^{5}+8q^{8}+(12+\cdots)q^{10}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(882))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(882)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)