Properties

Label 2760.2.k
Level $2760$
Weight $2$
Character orbit 2760.k
Rep. character $\chi_{2760}(2209,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $6$
Sturm bound $1152$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1152\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2760, [\chi])\).

Total New Old
Modular forms 592 68 524
Cusp forms 560 68 492
Eisenstein series 32 0 32

Trace form

\( 68q - 8q^{5} - 68q^{9} + O(q^{10}) \) \( 68q - 8q^{5} - 68q^{9} - 4q^{15} - 4q^{25} + 32q^{29} + 8q^{31} - 32q^{41} + 8q^{45} - 60q^{49} - 8q^{55} - 32q^{61} + 16q^{65} - 8q^{69} - 40q^{79} + 68q^{81} + 24q^{85} + 48q^{89} + 48q^{91} + 24q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2760, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2760.2.k.a \(2\) \(22.039\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2760.2.k.b \(2\) \(22.039\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1+2i)q^{5}-q^{9}+(2+i)q^{15}+\cdots\)
2760.2.k.c \(12\) \(22.039\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{10}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots\)
2760.2.k.d \(14\) \(22.039\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{2}q^{3}-\beta _{12}q^{5}+(\beta _{2}+\beta _{10})q^{7}+\cdots\)
2760.2.k.e \(16\) \(22.039\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{14}q^{11}+\cdots\)
2760.2.k.f \(22\) \(22.039\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)