Properties

Label 1340.2.i
Level 1340
Weight 2
Character orbit i
Rep. character \(\chi_{1340}(841,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 44
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1340, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1340.2.i.a \(2\) \(10.700\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(2\) \(1\) \(q+q^{3}+q^{5}+\zeta_{6}q^{7}-2q^{9}+6\zeta_{6}q^{11}+\cdots\)
1340.2.i.b \(8\) \(10.700\) 8.0.5808268944.1 None \(0\) \(2\) \(-8\) \(2\) \(q-\beta _{3}q^{3}-q^{5}+(\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
1340.2.i.c \(16\) \(10.700\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(-16\) \(0\) \(q-\beta _{6}q^{3}-q^{5}+\beta _{11}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1340.2.i.d \(18\) \(10.700\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-2\) \(18\) \(3\) \(q+(-\beta _{1}+\beta _{5})q^{3}+q^{5}-\beta _{10}q^{7}+(1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)