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Properties

Label 961.6.a
Level $961$
Weight $6$
Character orbit 961.a
Rep. character $\chi_{961}(1,\cdot)$
Character field $\Q$
Dimension $372$
Newform subspaces $13$
Sturm bound $496$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 961 = 31^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 961.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(496\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(961))\).

Total New Old
Modular forms 430 401 29
Cusp forms 398 372 26
Eisenstein series 32 29 3

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

\(31\)TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(211\)\(196\)\(15\)\(195\)\(182\)\(13\)\(16\)\(14\)\(2\)
\(-\)\(219\)\(205\)\(14\)\(203\)\(190\)\(13\)\(16\)\(15\)\(1\)

Trace form

\( 372 q + 2 q^{2} + 22 q^{3} + 5718 q^{4} - 56 q^{5} + 72 q^{6} + 20 q^{7} - 114 q^{8} + 27766 q^{9} - 1064 q^{10} + 664 q^{11} + 758 q^{12} + 288 q^{13} + 108 q^{14} - 78 q^{15} + 84110 q^{16} - 648 q^{17}+ \cdots + 49280 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(961))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 31
961.6.a.a 961.a 1.a $3$ $154.129$ 3.3.837.1 \(\Q(\sqrt{-31}) \) 961.6.a.a \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+(-4\beta _{1}+\beta _{2})q^{2}+(2^{5}-15\beta _{1}+14\beta _{2})q^{4}+\cdots\)
961.6.a.b 961.a 1.a $5$ $154.129$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 31.6.a.a \(-9\) \(20\) \(-72\) \(-108\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(4+\beta _{1}+\beta _{3})q^{3}+\cdots\)
961.6.a.c 961.a 1.a $8$ $154.129$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 31.6.a.b \(7\) \(2\) \(128\) \(88\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
961.6.a.d 961.a 1.a $10$ $154.129$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 961.6.a.d \(2\) \(0\) \(88\) \(216\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(11+2\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
961.6.a.e 961.a 1.a $12$ $154.129$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 31.6.c.a \(-2\) \(-10\) \(-28\) \(134\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(14+\beta _{1}+\cdots)q^{4}+\cdots\)
961.6.a.f 961.a 1.a $12$ $154.129$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 31.6.c.a \(-2\) \(10\) \(-28\) \(134\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(14+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
961.6.a.g 961.a 1.a $26$ $154.129$ None 961.6.a.g \(0\) \(0\) \(56\) \(196\) $-$ $\mathrm{SU}(2)$
961.6.a.h 961.a 1.a $26$ $154.129$ None 31.6.d.a \(1\) \(-34\) \(-33\) \(10\) $+$ $\mathrm{SU}(2)$
961.6.a.i 961.a 1.a $26$ $154.129$ None 31.6.d.a \(1\) \(34\) \(-33\) \(10\) $-$ $\mathrm{SU}(2)$
961.6.a.j 961.a 1.a $48$ $154.129$ None 31.6.g.a \(2\) \(-35\) \(33\) \(-134\) $+$ $\mathrm{SU}(2)$
961.6.a.k 961.a 1.a $48$ $154.129$ None 31.6.g.a \(2\) \(35\) \(33\) \(-134\) $-$ $\mathrm{SU}(2)$
961.6.a.l 961.a 1.a $52$ $154.129$ None 961.6.a.l \(32\) \(0\) \(200\) \(392\) $-$ $\mathrm{SU}(2)$
961.6.a.m 961.a 1.a $96$ $154.129$ None 961.6.a.m \(-32\) \(0\) \(-400\) \(-784\) $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(961))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(961)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)