Properties

Label 287.2.c
Level 287
Weight 2
Character orbit c
Rep. character \(\chi_{287}(204,\cdot)\)
Character field \(\Q\)
Dimension 22
Newforms 2
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(287, [\chi])\).

Total New Old
Modular forms 30 22 8
Cusp forms 26 22 4
Eisenstein series 4 0 4

Trace form

\( 22q + 24q^{4} - 8q^{5} - 12q^{8} - 14q^{9} + O(q^{10}) \) \( 22q + 24q^{4} - 8q^{5} - 12q^{8} - 14q^{9} + 4q^{10} + 12q^{16} - 20q^{18} - 20q^{20} - 4q^{21} + 12q^{23} + 30q^{25} + 8q^{31} - 24q^{32} + 16q^{33} - 16q^{36} - 32q^{37} - 36q^{39} - 20q^{40} - 6q^{41} + 24q^{42} - 32q^{43} + 56q^{45} - 22q^{49} - 4q^{50} + 12q^{51} + 12q^{57} - 36q^{59} + 24q^{61} + 24q^{62} + 16q^{64} + 56q^{66} - 18q^{72} - 64q^{73} + 30q^{74} - 8q^{77} + 66q^{78} - 36q^{80} + 6q^{81} + 18q^{82} + 40q^{83} - 26q^{84} + 60q^{86} - 28q^{87} - 96q^{90} + 26q^{92} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(287, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
287.2.c.a \(10\) \(2.292\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(4\) \(0\) \(-10\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
287.2.c.b \(12\) \(2.292\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(0\) \(2\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)