Properties

Label 1183.2.c
Level $1183$
Weight $2$
Character orbit 1183.c
Rep. character $\chi_{1183}(337,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $10$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(242\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 134 78 56
Cusp forms 106 78 28
Eisenstein series 28 0 28

Trace form

\( 78q - 80q^{4} + 86q^{9} + O(q^{10}) \) \( 78q - 80q^{4} + 86q^{9} + 8q^{10} + 28q^{12} + 4q^{14} + 68q^{16} + 8q^{17} - 32q^{22} - 4q^{23} - 90q^{25} + 12q^{27} + 12q^{29} - 8q^{30} + 4q^{35} - 88q^{36} + 4q^{38} - 4q^{40} + 4q^{42} + 44q^{43} - 24q^{48} - 78q^{49} - 8q^{51} - 4q^{53} - 28q^{55} - 12q^{56} - 28q^{61} - 4q^{62} - 48q^{64} - 52q^{66} - 32q^{68} + 20q^{69} - 4q^{74} - 28q^{75} - 16q^{77} - 36q^{79} + 94q^{81} + 84q^{82} + 32q^{87} + 88q^{88} + 60q^{90} + 16q^{92} - 60q^{94} - 48q^{95} + O(q^{100}) \)

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.c.a \(2\) \(9.446\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-2q^{3}+2q^{4}-3iq^{5}-iq^{7}+q^{9}+\cdots\)
1183.2.c.b \(2\) \(9.446\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}+3iq^{5}-iq^{7}-3q^{9}+\cdots\)
1183.2.c.c \(4\) \(9.446\) \(\Q(i, \sqrt{5})\) None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
1183.2.c.d \(4\) \(9.446\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+(3\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
1183.2.c.e \(4\) \(9.446\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{3})q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1183.2.c.f \(6\) \(9.446\) 6.0.399424.1 None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.c.g \(8\) \(9.446\) 8.0.\(\cdots\).1 None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1183.2.c.h \(12\) \(9.446\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-8\) \(0\) \(0\) \(q+(-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)
1183.2.c.i \(12\) \(9.446\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{7})q^{2}-\beta _{2}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
1183.2.c.j \(24\) \(9.446\) None \(0\) \(16\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)