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Properties

Label 1340.2.i
Level $1340$
Weight $2$
Character orbit 1340.i
Rep. character $\chi_{1340}(841,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $4$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
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 420 44 376
Cusp forms 396 44 352
Eisenstein series 24 0 24

Trace form

\( 44 q - 4 q^{5} + 6 q^{7} + 48 q^{9} + O(q^{10}) \) \( 44 q - 4 q^{5} + 6 q^{7} + 48 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{17} - 2 q^{19} + 6 q^{21} - 6 q^{23} + 44 q^{25} - 12 q^{27} - 12 q^{29} - 4 q^{33} + 2 q^{35} + 8 q^{37} + 22 q^{39} + 48 q^{43} - 8 q^{45} - 2 q^{47} - 24 q^{49} + 6 q^{51} + 16 q^{53} - 12 q^{55} + 26 q^{57} + 32 q^{59} + 12 q^{61} + 18 q^{63} - 4 q^{65} + 34 q^{67} - 2 q^{69} - 12 q^{71} - 6 q^{73} - 4 q^{77} + 12 q^{79} + 44 q^{81} + 6 q^{83} + 6 q^{85} + 30 q^{87} - 44 q^{89} + 56 q^{91} - 22 q^{93} + 18 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.i.a 1340.i 67.c $2$ $10.700$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}+q^{5}+\zeta_{6}q^{7}-2q^{9}+6\zeta_{6}q^{11}+\cdots\)
1340.2.i.b 1340.i 67.c $8$ $10.700$ 8.0.5808268944.1 None \(0\) \(2\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{3}-q^{5}+(\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
1340.2.i.c 1340.i 67.c $16$ $10.700$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{3}-q^{5}+\beta _{11}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1340.2.i.d 1340.i 67.c $18$ $10.700$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-2\) \(18\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}+q^{5}-\beta _{10}q^{7}+(1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)