Properties

Label 1287.2.b
Level $1287$
Weight $2$
Character orbit 1287.b
Rep. character $\chi_{1287}(298,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $4$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1287.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(336\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1287, [\chi])\).

Total New Old
Modular forms 176 56 120
Cusp forms 160 56 104
Eisenstein series 16 0 16

Trace form

\( 56q - 50q^{4} + O(q^{10}) \) \( 56q - 50q^{4} + 4q^{13} + 16q^{14} + 30q^{16} - 12q^{17} - 2q^{22} + 4q^{23} - 36q^{25} - 2q^{26} + 8q^{29} - 8q^{35} + 14q^{38} - 40q^{40} + 12q^{43} - 76q^{49} + 48q^{52} + 4q^{53} - 8q^{55} - 6q^{56} + 12q^{61} - 24q^{62} + 50q^{64} - 20q^{65} - 36q^{68} - 44q^{74} - 8q^{77} + 32q^{79} - 132q^{82} - 18q^{88} + 16q^{91} + 38q^{92} - 16q^{94} - 4q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1287, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1287.2.b.a \(10\) \(10.277\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\beta _{7}+\cdots)q^{5}+\cdots\)
1287.2.b.b \(12\) \(10.277\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{5})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
1287.2.b.c \(14\) \(10.277\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{5}+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1287.2.b.d \(20\) \(10.277\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{12}q^{2}+(-1-\beta _{8})q^{4}+(\beta _{10}+\beta _{11}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 2}\)