Properties

Label 1340.2.d
Level $1340$
Weight $2$
Character orbit 1340.d
Rep. character $\chi_{1340}(269,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $3$
Sturm bound $408$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1340.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(408\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1340, [\chi])\).

Total New Old
Modular forms 210 34 176
Cusp forms 198 34 164
Eisenstein series 12 0 12

Trace form

\( 34 q + 2 q^{5} - 42 q^{9} + O(q^{10}) \) \( 34 q + 2 q^{5} - 42 q^{9} - 4 q^{11} + 10 q^{15} - 2 q^{25} + 8 q^{31} - 14 q^{35} - 4 q^{41} - 2 q^{45} - 26 q^{49} + 28 q^{51} - 4 q^{59} - 4 q^{61} + 2 q^{65} + 8 q^{69} - 20 q^{71} - 18 q^{75} - 20 q^{79} + 74 q^{81} - 22 q^{85} + 8 q^{89} - 28 q^{91} - 32 q^{95} + 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1340, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1340.2.d.a 1340.d 5.b $2$ $10.700$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2+i)q^{5}+3iq^{7}+2q^{9}+\cdots\)
1340.2.d.b 1340.d 5.b $8$ $10.700$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+(2-\beta _{5})q^{5}+(-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
1340.2.d.c 1340.d 5.b $24$ $10.700$ None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)