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Properties

Label 1183.4.a
Level $1183$
Weight $4$
Character orbit 1183.a
Rep. character $\chi_{1183}(1,\cdot)$
Character field $\Q$
Dimension $233$
Newform subspaces $19$
Sturm bound $485$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(485\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1183))\).

Total New Old
Modular forms 378 233 145
Cusp forms 350 233 117
Eisenstein series 28 0 28

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
\(+\)\(+\)$+$\(60\)
\(+\)\(-\)$-$\(57\)
\(-\)\(+\)$-$\(53\)
\(-\)\(-\)$+$\(63\)
Plus space\(+\)\(123\)
Minus space\(-\)\(110\)

Trace form

\( 233 q - 5 q^{2} - 2 q^{3} + 929 q^{4} + 62 q^{6} - 7 q^{7} - 45 q^{8} + 2133 q^{9} + O(q^{10}) \) \( 233 q - 5 q^{2} - 2 q^{3} + 929 q^{4} + 62 q^{6} - 7 q^{7} - 45 q^{8} + 2133 q^{9} + 136 q^{10} + 40 q^{11} - 94 q^{12} + 63 q^{14} + 64 q^{15} + 3705 q^{16} + 110 q^{17} - 513 q^{18} - 158 q^{19} + 60 q^{20} - 98 q^{21} - 76 q^{22} + 356 q^{23} + 1186 q^{24} + 5359 q^{25} + 676 q^{27} + 49 q^{28} - 10 q^{29} - 32 q^{30} + 204 q^{31} - 425 q^{32} + 136 q^{33} + 54 q^{34} + 112 q^{35} + 8093 q^{36} + 530 q^{37} + 210 q^{38} - 628 q^{40} - 682 q^{41} + 154 q^{42} + 872 q^{43} - 460 q^{44} - 344 q^{45} + 1344 q^{46} + 748 q^{47} + 1294 q^{48} + 11417 q^{49} - 871 q^{50} + 700 q^{51} - 422 q^{53} + 980 q^{54} - 248 q^{55} + 567 q^{56} + 1868 q^{57} + 882 q^{58} - 790 q^{59} + 3204 q^{60} - 2072 q^{61} - 3200 q^{62} - 903 q^{63} + 17221 q^{64} - 2220 q^{66} - 92 q^{67} + 2966 q^{68} - 1560 q^{69} + 616 q^{70} - 2392 q^{71} - 1181 q^{72} - 1518 q^{73} + 4526 q^{74} - 550 q^{75} + 726 q^{76} + 896 q^{77} + 644 q^{79} - 1168 q^{80} + 20261 q^{81} + 630 q^{82} + 274 q^{83} - 910 q^{84} - 2552 q^{85} + 756 q^{86} - 4764 q^{87} + 564 q^{88} + 794 q^{89} + 1660 q^{90} - 2136 q^{92} + 2160 q^{93} - 304 q^{94} - 2000 q^{95} - 6 q^{96} + 1622 q^{97} - 245 q^{98} + 2632 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1183))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13
1183.4.a.a 1183.a 1.a $1$ $69.799$ \(\Q\) None \(-5\) \(2\) \(-19\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{2}+2q^{3}+17q^{4}-19q^{5}-10q^{6}+\cdots\)
1183.4.a.b 1183.a 1.a $1$ $69.799$ \(\Q\) None \(1\) \(-2\) \(-16\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
1183.4.a.c 1183.a 1.a $1$ $69.799$ \(\Q\) None \(5\) \(2\) \(19\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+2q^{3}+17q^{4}+19q^{5}+10q^{6}+\cdots\)
1183.4.a.d 1183.a 1.a $3$ $69.799$ 3.3.1384.1 None \(-1\) \(1\) \(22\) \(21\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1183.4.a.e 1183.a 1.a $4$ $69.799$ 4.4.5364412.1 None \(4\) \(-5\) \(36\) \(-28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
1183.4.a.f 1183.a 1.a $5$ $69.799$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-7\) \(-5\) \(-16\) \(35\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(10+\cdots)q^{4}+\cdots\)
1183.4.a.g 1183.a 1.a $6$ $69.799$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-2\) \(13\) \(-26\) \(-42\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1183.4.a.h 1183.a 1.a $9$ $69.799$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(-6\) \(3\) \(-63\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1183.4.a.i 1183.a 1.a $9$ $69.799$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-6\) \(-3\) \(63\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1183.4.a.j 1183.a 1.a $10$ $69.799$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-6\) \(4\) \(-14\) \(70\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.4.a.k 1183.a 1.a $10$ $69.799$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(6\) \(4\) \(14\) \(-70\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.4.a.l 1183.a 1.a $11$ $69.799$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-4\) \(0\) \(-22\) \(-77\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1183.4.a.m 1183.a 1.a $11$ $69.799$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(4\) \(0\) \(22\) \(77\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
1183.4.a.n 1183.a 1.a $22$ $69.799$ None \(-8\) \(0\) \(-44\) \(-154\) $+$ $-$ $\mathrm{SU}(2)$
1183.4.a.o 1183.a 1.a $22$ $69.799$ None \(8\) \(0\) \(44\) \(154\) $-$ $-$ $\mathrm{SU}(2)$
1183.4.a.p 1183.a 1.a $24$ $69.799$ None \(-3\) \(-19\) \(-10\) \(168\) $-$ $+$ $\mathrm{SU}(2)$
1183.4.a.q 1183.a 1.a $24$ $69.799$ None \(3\) \(-19\) \(10\) \(-168\) $+$ $-$ $\mathrm{SU}(2)$
1183.4.a.r 1183.a 1.a $30$ $69.799$ None \(-8\) \(17\) \(2\) \(-210\) $+$ $+$ $\mathrm{SU}(2)$
1183.4.a.s 1183.a 1.a $30$ $69.799$ None \(8\) \(17\) \(-2\) \(210\) $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1183))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1183)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)