Properties

Label 847.2.a
Level $847$
Weight $2$
Character orbit 847.a
Rep. character $\chi_{847}(1,\cdot)$
Character field $\Q$
Dimension $55$
Newform subspaces $16$
Sturm bound $176$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(176\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(847))\).

Total New Old
Modular forms 100 55 45
Cusp forms 77 55 22
Eisenstein series 23 0 23

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

\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(+\)\(10\)
Plus space\(+\)\(23\)
Minus space\(-\)\(32\)

Trace form

\( 55q - q^{2} - 4q^{3} + 59q^{4} + 2q^{5} + 8q^{6} - q^{7} + 3q^{8} + 47q^{9} + O(q^{10}) \) \( 55q - q^{2} - 4q^{3} + 59q^{4} + 2q^{5} + 8q^{6} - q^{7} + 3q^{8} + 47q^{9} + 2q^{10} - 16q^{12} + 2q^{13} + q^{14} - 8q^{15} + 55q^{16} + 2q^{17} + 19q^{18} + 6q^{20} - 4q^{21} + 4q^{23} + 16q^{24} + 57q^{25} - 18q^{26} - 16q^{27} - 7q^{28} - 6q^{29} - 16q^{30} - 16q^{31} - 5q^{32} + 6q^{34} - 2q^{35} + 43q^{36} + 2q^{37} - 24q^{38} - 8q^{39} - 6q^{40} + 10q^{41} + 12q^{42} - 28q^{43} - 2q^{45} - 16q^{46} - 20q^{47} - 8q^{48} + 55q^{49} + q^{50} - 4q^{51} - 18q^{52} - 10q^{53} + 24q^{54} - 3q^{56} - 4q^{57} - 30q^{58} - 20q^{60} + 22q^{61} - 20q^{62} + 3q^{63} + 83q^{64} + 20q^{65} - 36q^{67} + 2q^{68} - 16q^{69} - 14q^{70} + 23q^{72} + 2q^{73} + 26q^{74} - 32q^{75} - 20q^{76} - 28q^{78} - 4q^{79} - 54q^{80} + 15q^{81} - 14q^{82} - 28q^{83} + 24q^{85} - 44q^{86} + 60q^{87} - 2q^{89} - 38q^{90} + 2q^{91} - 36q^{92} - 32q^{93} + 20q^{94} - 4q^{95} - 40q^{96} - 10q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(847))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 11
847.2.a.a \(1\) \(6.763\) \(\Q\) None \(-1\) \(2\) \(-2\) \(1\) \(-\) \(-\) \(q-q^{2}+2q^{3}-q^{4}-2q^{5}-2q^{6}+q^{7}+\cdots\)
847.2.a.b \(1\) \(6.763\) \(\Q\) None \(0\) \(-3\) \(-1\) \(1\) \(-\) \(-\) \(q-3q^{3}-2q^{4}-q^{5}+q^{7}+6q^{9}+6q^{12}+\cdots\)
847.2.a.c \(1\) \(6.763\) \(\Q\) None \(0\) \(1\) \(3\) \(-1\) \(+\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}-q^{7}-2q^{9}-2q^{12}+\cdots\)
847.2.a.d \(2\) \(6.763\) \(\Q(\sqrt{5}) \) None \(-3\) \(-1\) \(2\) \(2\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+(-1+\beta )q^{3}+3\beta q^{4}+\cdots\)
847.2.a.e \(2\) \(6.763\) \(\Q(\sqrt{13}) \) None \(-1\) \(-1\) \(0\) \(2\) \(-\) \(-\) \(q-\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
847.2.a.f \(2\) \(6.763\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-4\) \(-2\) \(+\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+3q^{4}-2q^{5}+(5+\cdots)q^{6}+\cdots\)
847.2.a.g \(2\) \(6.763\) \(\Q(\sqrt{13}) \) None \(1\) \(-1\) \(0\) \(-2\) \(+\) \(-\) \(q+\beta q^{2}-\beta q^{3}+(1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
847.2.a.h \(2\) \(6.763\) \(\Q(\sqrt{5}) \) None \(3\) \(-1\) \(2\) \(-2\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(-1+\beta )q^{3}+3\beta q^{4}+\cdots\)
847.2.a.i \(3\) \(6.763\) 3.3.568.1 None \(-2\) \(-1\) \(1\) \(-3\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots\)
847.2.a.j \(3\) \(6.763\) 3.3.568.1 None \(2\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots\)
847.2.a.k \(4\) \(6.763\) 4.4.2525.1 None \(-2\) \(-2\) \(-6\) \(4\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
847.2.a.l \(4\) \(6.763\) 4.4.2525.1 None \(2\) \(-2\) \(-6\) \(-4\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
847.2.a.m \(6\) \(6.763\) 6.6.7674048.1 None \(-4\) \(-2\) \(-4\) \(-6\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
847.2.a.n \(6\) \(6.763\) 6.6.7674048.1 None \(4\) \(-2\) \(-4\) \(6\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
847.2.a.o \(8\) \(6.763\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(4\) \(10\) \(-8\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
847.2.a.p \(8\) \(6.763\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(4\) \(10\) \(8\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(847))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(847)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)