Properties

Label 1143.2.a
Level $1143$
Weight $2$
Character orbit 1143.a
Rep. character $\chi_{1143}(1,\cdot)$
Character field $\Q$
Dimension $53$
Newform subspaces $11$
Sturm bound $256$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1143 = 3^{2} \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1143.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(256\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1143))\).

Total New Old
Modular forms 132 53 79
Cusp forms 125 53 72
Eisenstein series 7 0 7

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

\(3\)\(127\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(18\)
\(-\)\(-\)\(+\)\(13\)
Plus space\(+\)\(19\)
Minus space\(-\)\(34\)

Trace form

\( 53q + 50q^{4} + 4q^{5} + 2q^{7} + 6q^{8} + O(q^{10}) \) \( 53q + 50q^{4} + 4q^{5} + 2q^{7} + 6q^{8} + 4q^{10} - 8q^{11} + 6q^{13} + 44q^{16} + 4q^{17} + 2q^{19} + 12q^{20} + 2q^{22} + 10q^{23} + 63q^{25} + 16q^{26} + 12q^{28} + 6q^{29} + 4q^{31} + 27q^{32} + 5q^{34} + 4q^{35} + 4q^{37} - q^{38} + 8q^{40} + 10q^{43} - 19q^{44} - 26q^{46} - 22q^{47} + 63q^{49} + 8q^{50} + 7q^{52} - 6q^{53} + 6q^{55} - 16q^{56} - 18q^{58} - 4q^{59} + 6q^{61} + 45q^{62} + 2q^{64} + 22q^{65} + 16q^{67} - 6q^{68} - 22q^{70} - 46q^{71} + 22q^{73} + 21q^{74} + 4q^{76} + 12q^{77} - 6q^{79} + 88q^{80} - 4q^{82} - 18q^{83} - 6q^{85} - 24q^{86} - 33q^{88} + 18q^{89} - 20q^{91} + 62q^{92} - 66q^{94} + 48q^{95} + 66q^{97} + 38q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1143))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 127
1143.2.a.a \(1\) \(9.127\) \(\Q\) None \(-2\) \(0\) \(-3\) \(-4\) \(-\) \(+\) \(q-2q^{2}+2q^{4}-3q^{5}-4q^{7}+6q^{10}+\cdots\)
1143.2.a.b \(1\) \(9.127\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(q-2q^{4}-q^{5}+4q^{11}+q^{13}+4q^{16}+\cdots\)
1143.2.a.c \(1\) \(9.127\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(q-2q^{4}+q^{5}-2q^{7}+4q^{11}-3q^{13}+\cdots\)
1143.2.a.d \(1\) \(9.127\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(+\) \(q-2q^{4}+q^{5}-4q^{11}+q^{13}+4q^{16}+\cdots\)
1143.2.a.e \(3\) \(9.127\) \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(6\) \(-3\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
1143.2.a.f \(4\) \(9.127\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(q+(\beta _{1}+\beta _{3})q^{2}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1143.2.a.g \(5\) \(9.127\) 5.5.246832.1 None \(-2\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1143.2.a.h \(5\) \(9.127\) 5.5.81509.1 None \(1\) \(0\) \(5\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)
1143.2.a.i \(7\) \(9.127\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-2\) \(0\) \(-8\) \(-3\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1143.2.a.j \(9\) \(9.127\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(2\) \(0\) \(4\) \(10\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(1-\beta _{8})q^{7}+\cdots\)
1143.2.a.k \(16\) \(9.127\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(10\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1143))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1143)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(381))\)\(^{\oplus 2}\)