Properties

Label 1040.2.k
Level $1040$
Weight $2$
Character orbit 1040.k
Rep. character $\chi_{1040}(961,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $5$
Sturm bound $336$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).

Total New Old
Modular forms 180 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

Trace form

\( 28q - 4q^{3} + 28q^{9} + O(q^{10}) \) \( 28q - 4q^{3} + 28q^{9} - 12q^{23} - 28q^{25} + 8q^{27} - 12q^{35} + 28q^{39} + 44q^{43} - 4q^{49} - 24q^{51} - 8q^{53} + 8q^{55} - 8q^{61} - 4q^{65} + 32q^{69} + 4q^{75} - 24q^{77} + 16q^{79} + 28q^{81} - 20q^{91} - 16q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1040.2.k.a \(2\) \(8.304\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots\)
1040.2.k.b \(6\) \(8.304\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
1040.2.k.c \(6\) \(8.304\) 6.0.9144576.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
1040.2.k.d \(6\) \(8.304\) 6.0.5089536.1 None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.k.e \(8\) \(8.304\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)