Properties

Label 1127.2.a
Level $1127$
Weight $2$
Character orbit 1127.a
Rep. character $\chi_{1127}(1,\cdot)$
Character field $\Q$
Dimension $75$
Newform subspaces $15$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1127.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1127))\).

Total New Old
Modular forms 120 75 45
Cusp forms 105 75 30
Eisenstein series 15 0 15

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

\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(25\)
\(-\)\(+\)\(-\)\(23\)
\(-\)\(-\)\(+\)\(14\)
Plus space\(+\)\(27\)
Minus space\(-\)\(48\)

Trace form

\( 75q + 2q^{2} + 74q^{4} + 4q^{5} + 3q^{6} + 3q^{8} + 77q^{9} + O(q^{10}) \) \( 75q + 2q^{2} + 74q^{4} + 4q^{5} + 3q^{6} + 3q^{8} + 77q^{9} + 4q^{10} - 2q^{11} + q^{12} - 4q^{13} - 14q^{15} + 72q^{16} + 4q^{17} + 17q^{18} - 4q^{19} + 10q^{20} - 6q^{22} + 3q^{23} + 14q^{24} + 73q^{25} + 11q^{26} - 12q^{27} + 4q^{29} + 18q^{30} - 24q^{31} - 12q^{32} + 14q^{33} + 6q^{34} + 69q^{36} + 28q^{37} + 42q^{38} + 32q^{40} + 12q^{41} + 40q^{43} + 10q^{45} + 2q^{46} - 16q^{47} - 3q^{48} + 22q^{50} - 22q^{51} + 3q^{52} + 18q^{53} - 11q^{54} + 24q^{57} + 9q^{58} - 4q^{59} - 80q^{60} + 2q^{61} - 9q^{62} + 11q^{64} + 66q^{65} - 14q^{66} + 6q^{67} - 36q^{68} - 4q^{69} - 52q^{71} + 11q^{72} + 8q^{75} - 66q^{76} - 75q^{78} - 32q^{79} + 16q^{80} + 75q^{81} + 31q^{82} - 6q^{83} + 56q^{85} - 88q^{86} + 28q^{87} + 2q^{88} + 22q^{89} - 50q^{90} + 6q^{92} + 22q^{93} + 27q^{94} - 60q^{95} + 3q^{96} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 23
1127.2.a.a \(1\) \(8.999\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q-q^{2}-q^{4}-2q^{5}+3q^{8}-3q^{9}+2q^{10}+\cdots\)
1127.2.a.b \(2\) \(8.999\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}-q^{4}-\beta q^{5}+\beta q^{6}+3q^{8}+\cdots\)
1127.2.a.c \(2\) \(8.999\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1127.2.a.d \(2\) \(8.999\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
1127.2.a.e \(2\) \(8.999\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+q^{2}+\beta q^{3}-q^{4}+\beta q^{5}+\beta q^{6}-3q^{8}+\cdots\)
1127.2.a.f \(3\) \(8.999\) 3.3.148.1 None \(-1\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
1127.2.a.g \(4\) \(8.999\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
1127.2.a.h \(5\) \(8.999\) 5.5.2147108.1 None \(2\) \(0\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots\)
1127.2.a.i \(6\) \(8.999\) 6.6.2803712.1 None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1127.2.a.j \(6\) \(8.999\) 6.6.89672832.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{2}+\beta _{4}q^{3}+(2+\beta _{5})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
1127.2.a.k \(7\) \(8.999\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-5\) \(-4\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1127.2.a.l \(7\) \(8.999\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(-4\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1127.2.a.m \(7\) \(8.999\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(4\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1127.2.a.n \(7\) \(8.999\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(5\) \(4\) \(0\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1127.2.a.o \(14\) \(8.999\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(6\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-\beta _{9}q^{2}+\beta _{1}q^{3}+(2+\beta _{7})q^{4}+\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1127))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1127)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)