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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13
1183.2.a.a 1183.a 1.a $1$ $9.446$ \(\Q\) None 91.2.a.b \(0\) \(-2\) \(3\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
1183.2.a.b 1183.a 1.a $1$ $9.446$ \(\Q\) None 91.2.a.a \(2\) \(0\) \(3\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots\)
1183.2.a.c 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{5}) \) None 91.2.f.a \(-3\) \(-3\) \(-3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.d 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{2}) \) None 91.2.a.c \(0\) \(0\) \(-6\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots\)
1183.2.a.e 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{3}) \) None 91.2.f.b \(0\) \(2\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
1183.2.a.f 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{3}) \) None 91.2.f.b \(0\) \(2\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
1183.2.a.g 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{5}) \) None 91.2.f.a \(3\) \(-3\) \(3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.h 1183.a 1.a $3$ $9.446$ 3.3.148.1 None 91.2.c.a \(-2\) \(0\) \(-3\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.i 1183.a 1.a $3$ $9.446$ 3.3.316.1 None 91.2.a.d \(-1\) \(-2\) \(-2\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1183.2.a.j 1183.a 1.a $3$ $9.446$ 3.3.148.1 None 91.2.c.a \(2\) \(0\) \(3\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.k 1183.a 1.a $4$ $9.446$ 4.4.27004.1 None 91.2.f.c \(-1\) \(1\) \(-7\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.l 1183.a 1.a $4$ $9.446$ 4.4.27004.1 None 91.2.f.c \(1\) \(1\) \(7\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.m 1183.a 1.a $6$ $9.446$ 6.6.7674048.1 None 91.2.q.a \(-4\) \(0\) \(-6\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.n 1183.a 1.a $6$ $9.446$ 6.6.1279733.1 None 1183.2.a.n \(-2\) \(-4\) \(-2\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
1183.2.a.o 1183.a 1.a $6$ $9.446$ 6.6.1279733.1 None 1183.2.a.n \(2\) \(-4\) \(2\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1183.2.a.p 1183.a 1.a $6$ $9.446$ 6.6.7674048.1 None 91.2.q.a \(4\) \(0\) \(6\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.q 1183.a 1.a $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1183.2.a.q \(-3\) \(8\) \(4\) \(-12\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.a.r 1183.a 1.a $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1183.2.a.q \(3\) \(8\) \(-4\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

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