Properties

Label 1183.2.e
Level $1183$
Weight $2$
Character orbit 1183.e
Rep. character $\chi_{1183}(170,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $184$
Newform subspaces $12$
Sturm bound $242$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(242\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1183, [\chi])\).

Total New Old
Modular forms 272 228 44
Cusp forms 216 184 32
Eisenstein series 56 44 12

Trace form

\( 184 q + 2 q^{2} - 78 q^{4} + 2 q^{5} + 6 q^{7} - 72 q^{9} + O(q^{10}) \) \( 184 q + 2 q^{2} - 78 q^{4} + 2 q^{5} + 6 q^{7} - 72 q^{9} - 10 q^{10} + 2 q^{11} - 10 q^{12} - 16 q^{14} + 20 q^{15} - 42 q^{16} - 2 q^{17} + 8 q^{19} - 32 q^{20} - 2 q^{21} - 32 q^{22} - 10 q^{23} + 20 q^{24} - 50 q^{25} - 60 q^{27} - 30 q^{28} + 16 q^{29} - 16 q^{30} + 4 q^{31} + 12 q^{32} + 8 q^{33} + 32 q^{34} + 16 q^{35} + 28 q^{36} + 8 q^{37} - 14 q^{38} - 4 q^{40} - 28 q^{41} - 30 q^{42} + 28 q^{43} - 6 q^{44} - 32 q^{45} + 20 q^{46} + 2 q^{47} + 188 q^{48} + 26 q^{49} - 8 q^{50} - 18 q^{51} + 18 q^{54} - 8 q^{55} + 8 q^{56} + 32 q^{57} - 42 q^{58} + 10 q^{59} - 44 q^{60} - 14 q^{61} + 72 q^{62} - 40 q^{63} - 8 q^{64} + 4 q^{66} + 4 q^{67} + 84 q^{68} - 64 q^{69} - 54 q^{70} - 20 q^{71} - 22 q^{72} + 22 q^{73} - 34 q^{74} - 24 q^{75} - 48 q^{76} + 36 q^{77} - 6 q^{79} + 70 q^{80} - 28 q^{81} + 20 q^{82} - 12 q^{83} + 98 q^{84} + 4 q^{85} + 54 q^{86} - 80 q^{87} + 30 q^{88} - 4 q^{89} + 196 q^{90} - 40 q^{92} + 18 q^{93} + 48 q^{94} - 14 q^{95} - 22 q^{96} + 68 q^{97} - 34 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1183, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1183.2.e.a 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.b 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
1183.2.e.c 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.d 1183.e 7.c $4$ $9.446$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
1183.2.e.e 1183.e 7.c $4$ $9.446$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots\)
1183.2.e.f 1183.e 7.c $10$ $9.446$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\cdots\)
1183.2.e.g 1183.e 7.c $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(1\) \(-1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.h 1183.e 7.c $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(1\) \(1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.i 1183.e 7.c $16$ $9.446$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{9}q^{2}+(-1-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.e.j 1183.e 7.c $24$ $9.446$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$
1183.2.e.k 1183.e 7.c $48$ $9.446$ None \(-1\) \(0\) \(13\) \(-3\) $\mathrm{SU}(2)[C_{3}]$
1183.2.e.l 1183.e 7.c $48$ $9.446$ None \(1\) \(0\) \(-13\) \(3\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1183, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)