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 $3$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1183.2.e.a \(2\) \(9.446\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-3\) \(1\) \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.b \(2\) \(9.446\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
1183.2.e.c \(2\) \(9.446\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(3\) \(-1\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.d \(4\) \(9.446\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(0\) \(0\) \(8\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
1183.2.e.e \(4\) \(9.446\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots\)
1183.2.e.f \(10\) \(9.446\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(2\) \(-1\) \(q+(-\beta _{1}+\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\cdots\)
1183.2.e.g \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(1\) \(-1\) \(6\) \(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.h \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(1\) \(1\) \(-6\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.i \(16\) \(9.446\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(-1-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.e.j \(24\) \(9.446\) None \(0\) \(-6\) \(0\) \(0\)
1183.2.e.k \(48\) \(9.446\) None \(-1\) \(0\) \(13\) \(-3\)
1183.2.e.l \(48\) \(9.446\) None \(1\) \(0\) \(-13\) \(3\)

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

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