Properties

Label 310.2.a
Level $310$
Weight $2$
Character orbit 310.a
Rep. character $\chi_{310}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $5$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 310 = 2 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 310.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(310))\).

Total New Old
Modular forms 52 9 43
Cusp forms 45 9 36
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.

\(2\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9 q + q^{2} + 9 q^{4} + q^{5} + 4 q^{6} - 8 q^{7} + q^{8} + 13 q^{9} + q^{10} + 4 q^{11} - 14 q^{13} + 4 q^{15} + 9 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} + q^{20} - 16 q^{21} - 16 q^{23} + 4 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(310))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 31
310.2.a.a 310.a 1.a $1$ $2.475$ \(\Q\) None 310.2.a.a \(1\) \(-2\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-4q^{7}+\cdots\)
310.2.a.b 310.a 1.a $1$ $2.475$ \(\Q\) None 310.2.a.b \(1\) \(2\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
310.2.a.c 310.a 1.a $2$ $2.475$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(-2\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
310.2.a.d 310.a 1.a $2$ $2.475$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(-2\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2q^{7}+\cdots\)
310.2.a.e 310.a 1.a $3$ $2.475$ 3.3.148.1 None 310.2.a.e \(3\) \(2\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(310)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)