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

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

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

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