Properties

Label 308.2.a
Level 308
Weight 2
Character orbit a
Rep. character \(\chi_{308}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 3
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 308.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(308))\).

Total New Old
Modular forms 54 6 48
Cusp forms 43 6 37
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.

\(2\)\(7\)\(11\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(1\)
Minus space\(-\)\(5\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 22q^{59} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 44q^{75} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(308))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 11
308.2.a.a \(1\) \(2.459\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots\)
308.2.a.b \(2\) \(2.459\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{3}+2q^{5}-q^{7}+3q^{9}-q^{11}+\cdots\)
308.2.a.c \(3\) \(2.459\) 3.3.1016.1 None \(0\) \(-1\) \(-1\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(308))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(308)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)