Properties

Label 1340.2.a
Level 1340
Weight 2
Character orbit a
Rep. character \(\chi_{1340}(1,\cdot)\)
Character field \(\Q\)
Dimension 22
Newforms 9
Sturm bound 408
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1340.a (trivial)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(408\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1340))\).

Total New Old
Modular forms 210 22 188
Cusp forms 199 22 177
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(67\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(11\)
Minus space\(-\)\(11\)

Trace form

\(22q \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut -\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 42q^{49} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut +\mathstrut 14q^{89} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut 24q^{97} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1340))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 67
1340.2.a.a \(1\) \(10.700\) \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
1340.2.a.b \(1\) \(10.700\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}-6q^{11}+2q^{13}+\cdots\)
1340.2.a.c \(1\) \(10.700\) \(\Q\) None \(0\) \(1\) \(-1\) \(5\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+5q^{7}-2q^{9}+2q^{13}+\cdots\)
1340.2.a.d \(2\) \(10.700\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-3\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1340.2.a.e \(2\) \(10.700\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)
1340.2.a.f \(3\) \(10.700\) \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+q^{5}+(1-3\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1340.2.a.g \(3\) \(10.700\) 3.3.257.1 None \(0\) \(4\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
1340.2.a.h \(4\) \(10.700\) 4.4.60513.1 None \(0\) \(-1\) \(4\) \(5\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1340.2.a.i \(5\) \(10.700\) 5.5.1465016.1 None \(0\) \(-2\) \(-5\) \(-10\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(-2+\beta _{2})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1340))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1340)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 2}\)