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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
882.4.a.a 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(-22\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-22q^{5}-8q^{8}+44q^{10}+\cdots\)
882.4.a.b 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(-12\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-12q^{5}-8q^{8}+24q^{10}+\cdots\)
882.4.a.c 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(-9\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-9q^{5}-8q^{8}+18q^{10}+\cdots\)
882.4.a.d 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+2q^{5}-8q^{8}-4q^{10}+\cdots\)
882.4.a.e 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+6q^{5}-8q^{8}-12q^{10}+\cdots\)
882.4.a.f 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(9\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+9q^{5}-8q^{8}-18q^{10}+\cdots\)
882.4.a.g 882.a 1.a $1$ $52.040$ \(\Q\) None \(-2\) \(0\) \(18\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+18q^{5}-8q^{8}-6^{2}q^{10}+\cdots\)
882.4.a.h 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-15\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-15q^{5}+8q^{8}-30q^{10}+\cdots\)
882.4.a.i 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-14\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-14q^{5}+8q^{8}-28q^{10}+\cdots\)
882.4.a.j 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-8\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-8q^{5}+8q^{8}-2^{4}q^{10}+\cdots\)
882.4.a.k 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-7\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-7q^{5}+8q^{8}-14q^{10}+\cdots\)
882.4.a.l 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\cdots\)
882.4.a.m 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-6q^{5}+8q^{8}-12q^{10}+\cdots\)
882.4.a.n 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\cdots\)
882.4.a.o 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+6q^{5}+8q^{8}+12q^{10}+\cdots\)
882.4.a.p 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(7\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+7q^{5}+8q^{8}+14q^{10}+\cdots\)
882.4.a.q 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(8\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+8q^{5}+8q^{8}+2^{4}q^{10}+\cdots\)
882.4.a.r 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(15\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+15q^{5}+8q^{8}+30q^{10}+\cdots\)
882.4.a.s 882.a 1.a $1$ $52.040$ \(\Q\) None \(2\) \(0\) \(22\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+22q^{5}+8q^{8}+44q^{10}+\cdots\)
882.4.a.t 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(-12\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-6+\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.u 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{193}) \) None \(-4\) \(0\) \(-7\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-3-\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.v 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{1345}) \) None \(-4\) \(0\) \(-5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(-2-\beta )q^{5}-8q^{8}+\cdots\)
882.4.a.w 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{22}) \) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}-2\beta q^{10}+\cdots\)
882.4.a.x 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{58}) \) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}-2\beta q^{10}+\cdots\)
882.4.a.y 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+5\beta q^{5}-8q^{8}-10\beta q^{10}+\cdots\)
882.4.a.z 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{1345}) \) None \(-4\) \(0\) \(5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(3-\beta )q^{5}-8q^{8}+(-6+\cdots)q^{10}+\cdots\)
882.4.a.ba 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{193}) \) None \(-4\) \(0\) \(7\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(4-\beta )q^{5}-8q^{8}+(-8+\cdots)q^{10}+\cdots\)
882.4.a.bb 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(-4\) \(0\) \(12\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+(6+\beta )q^{5}-8q^{8}+(-12+\cdots)q^{10}+\cdots\)
882.4.a.bc 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(-12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-6+\beta )q^{5}+8q^{8}+\cdots\)
882.4.a.bd 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{193}) \) None \(4\) \(0\) \(-7\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(-3-\beta )q^{5}+8q^{8}+\cdots\)
882.4.a.be 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+5\beta q^{5}+8q^{8}+10\beta q^{10}+\cdots\)
882.4.a.bf 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{58}) \) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+2\beta q^{10}+\cdots\)
882.4.a.bg 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+14\beta q^{5}+8q^{8}+28\beta q^{10}+\cdots\)
882.4.a.bh 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{193}) \) None \(4\) \(0\) \(7\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(4-\beta )q^{5}+8q^{8}+(8+\cdots)q^{10}+\cdots\)
882.4.a.bi 882.a 1.a $2$ $52.040$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+(6+\beta )q^{5}+8q^{8}+(12+\cdots)q^{10}+\cdots\)

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

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