Properties

Label 268.2.a
Level 268
Weight 2
Character orbit a
Rep. character \(\chi_{268}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 3
Sturm bound 68
Trace bound 3

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Defining parameters

Level: \( N \) = \( 268 = 2^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 268.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(68\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(268))\).

Total New Old
Modular forms 37 5 32
Cusp forms 32 5 27
Eisenstein series 5 0 5

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

\(2\)\(67\)FrickeDim.
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 5q^{23} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut +\mathstrut 3q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 19q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 5q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 6q^{75} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 19q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 17q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 34q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(268))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 67
268.2.a.a \(1\) \(2.140\) \(\Q\) None \(0\) \(2\) \(2\) \(2\) \(-\) \(+\) \(q+2q^{3}+2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
268.2.a.b \(2\) \(2.140\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(-5\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
268.2.a.c \(2\) \(2.140\) \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(-2\) \(1\) \(-\) \(+\) \(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(268))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(268)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 2}\)