Properties

Label 1336.2.a
Level 1336
Weight 2
Character orbit a
Rep. character \(\chi_{1336}(1,\cdot)\)
Character field \(\Q\)
Dimension 42
Newforms 5
Sturm bound 336
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1336 = 2^{3} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1336.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1336))\).

Total New Old
Modular forms 172 42 130
Cusp forms 165 42 123
Eisenstein series 7 0 7

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

\(2\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(24\)

Trace form

\(42q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(42q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 38q^{49} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 36q^{63} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 30q^{67} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 32q^{87} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 167
1336.2.a.a \(2\) \(10.668\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(0\) \(-7\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(1-2\beta )q^{5}+(-4+\beta )q^{7}+\cdots\)
1336.2.a.b \(7\) \(10.668\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-6\) \(0\) \(-1\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1336.2.a.c \(9\) \(10.668\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-1\) \(-8\) \(2\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1336.2.a.d \(12\) \(10.668\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-1\) \(8\) \(-4\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(1-\beta _{9})q^{5}+\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots\)
1336.2.a.e \(12\) \(10.668\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(5\) \(-2\) \(10\) \(+\) \(-\) \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(1+\beta _{11})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1336))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1336)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 2}\)