Properties

Label 1183.2.a
Level $1183$
Weight $2$
Character orbit 1183.a
Rep. character $\chi_{1183}(1,\cdot)$
Character field $\Q$
Dimension $77$
Newform subspaces $18$
Sturm bound $242$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(242\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1183))\).

Total New Old
Modular forms 134 77 57
Cusp forms 107 77 30
Eisenstein series 27 0 27

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

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(17\)
\(+\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(24\)
\(-\)\(-\)\(+\)\(15\)
Plus space\(+\)\(32\)
Minus space\(-\)\(45\)

Trace form

\( 77q + q^{2} + 4q^{3} + 81q^{4} - 2q^{5} + q^{7} - 3q^{8} + 81q^{9} + O(q^{10}) \) \( 77q + q^{2} + 4q^{3} + 81q^{4} - 2q^{5} + q^{7} - 3q^{8} + 81q^{9} - 10q^{10} + 4q^{11} - q^{14} + 4q^{15} + 85q^{16} - 2q^{17} + 9q^{18} + 12q^{19} + 2q^{20} - 4q^{22} - 12q^{23} + 4q^{24} + 67q^{25} + 4q^{27} + 7q^{28} - 18q^{29} - 16q^{30} + 4q^{31} - 15q^{32} + 4q^{33} - 2q^{34} - 6q^{35} + 93q^{36} + 6q^{37} + 8q^{38} - 14q^{40} - 2q^{41} + 8q^{42} - 16q^{43} - 22q^{45} + 16q^{46} - 8q^{47} - 28q^{48} + 77q^{49} - q^{50} - 8q^{51} + 14q^{53} - 48q^{54} - 28q^{55} + 3q^{56} - 30q^{58} - 16q^{59} + 20q^{60} + 14q^{61} - 4q^{62} + 5q^{63} + 73q^{64} - 36q^{66} + 16q^{67} - 54q^{68} + 4q^{69} - 6q^{70} + 32q^{71} + q^{72} + 22q^{73} - 54q^{74} + 32q^{75} - 16q^{76} - 4q^{77} - 12q^{79} + 38q^{80} + 77q^{81} - 42q^{82} - 24q^{83} - 16q^{84} + 8q^{85} + 24q^{86} + 8q^{87} - 84q^{88} - 26q^{89} + 2q^{90} - 8q^{92} + 20q^{93} - 20q^{94} - 16q^{95} + 4q^{96} + 6q^{97} + q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
1183.2.a.a \(1\) \(9.446\) \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) \(+\) \(+\) \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
1183.2.a.b \(1\) \(9.446\) \(\Q\) None \(2\) \(0\) \(3\) \(1\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots\)
1183.2.a.c \(2\) \(9.446\) \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-3\) \(-2\) \(+\) \(+\) \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.d \(2\) \(9.446\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(-2\) \(+\) \(+\) \(q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots\)
1183.2.a.e \(2\) \(9.446\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(+\) \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
1183.2.a.f \(2\) \(9.446\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
1183.2.a.g \(2\) \(9.446\) \(\Q(\sqrt{5}) \) None \(3\) \(-3\) \(3\) \(2\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.h \(3\) \(9.446\) 3.3.148.1 None \(-2\) \(0\) \(-3\) \(3\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.i \(3\) \(9.446\) 3.3.316.1 None \(-1\) \(-2\) \(-2\) \(3\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1183.2.a.j \(3\) \(9.446\) 3.3.148.1 None \(2\) \(0\) \(3\) \(-3\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.k \(4\) \(9.446\) 4.4.27004.1 None \(-1\) \(1\) \(-7\) \(-4\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.l \(4\) \(9.446\) 4.4.27004.1 None \(1\) \(1\) \(7\) \(4\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.m \(6\) \(9.446\) 6.6.7674048.1 None \(-4\) \(0\) \(-6\) \(6\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.n \(6\) \(9.446\) 6.6.1279733.1 None \(-2\) \(-4\) \(-2\) \(6\) \(-\) \(-\) \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
1183.2.a.o \(6\) \(9.446\) 6.6.1279733.1 None \(2\) \(-4\) \(2\) \(-6\) \(+\) \(+\) \(q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1183.2.a.p \(6\) \(9.446\) 6.6.7674048.1 None \(4\) \(0\) \(6\) \(-6\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.q \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(8\) \(4\) \(-12\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.a.r \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(8\) \(-4\) \(12\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)