Properties

Label 1040.2.dh
Level $1040$
Weight $2$
Character orbit 1040.dh
Rep. character $\chi_{1040}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
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.dh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
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 360 88 272
Cusp forms 312 80 232
Eisenstein series 48 8 40

Trace form

\( 80 q - 2 q^{5} + 34 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{5} + 34 q^{9} + 2 q^{11} - 2 q^{15} + 2 q^{19} - 20 q^{21} - 2 q^{25} + 8 q^{31} - 4 q^{35} - 2 q^{39} - 8 q^{41} - 7 q^{45} + 22 q^{49} + 92 q^{51} + 2 q^{55} - 6 q^{59} - 12 q^{61} - 7 q^{65} - 14 q^{69} - 26 q^{71} + 6 q^{75} - 36 q^{81} - 7 q^{85} + 14 q^{89} - 14 q^{91} + 8 q^{95} - 104 q^{99} + O(q^{100}) \)

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.dh.a $12$ $8.304$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{1}+\beta _{10})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\beta _{2}q^{7}+\cdots\)
1040.2.dh.b $12$ $8.304$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{9})q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(-2\beta _{3}+\cdots)q^{7}+\cdots\)
1040.2.dh.c $12$ $8.304$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{10})q^{3}-\beta _{9}q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots\)
1040.2.dh.d $44$ $8.304$ None \(0\) \(0\) \(4\) \(0\)

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

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