Properties

Label 462.2.a
Level $462$
Weight $2$
Character orbit 462.a
Rep. character $\chi_{462}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $8$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(462))\).

Total New Old
Modular forms 104 9 95
Cusp forms 89 9 80
Eisenstein series 15 0 15

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

\(2\)\(3\)\(7\)\(11\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)\(1\)\(2\)\(3\)\(1\)\(2\)\(0\)\(0\)\(0\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)\(1\)\(8\)\(8\)\(1\)\(7\)\(1\)\(0\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(8\)\(0\)\(8\)\(7\)\(0\)\(7\)\(1\)\(0\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)\(1\)\(4\)\(4\)\(1\)\(3\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)\(1\)\(8\)\(8\)\(1\)\(7\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)\(0\)\(5\)\(4\)\(0\)\(4\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)\(0\)\(6\)\(5\)\(0\)\(5\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)\(2\)\(5\)\(6\)\(2\)\(4\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)\(0\)\(5\)\(4\)\(0\)\(4\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)\(0\)\(8\)\(7\)\(0\)\(7\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(9\)\(1\)\(8\)\(8\)\(1\)\(7\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)\(0\)\(5\)\(4\)\(0\)\(4\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)\(0\)\(7\)\(6\)\(0\)\(6\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)\(1\)\(5\)\(5\)\(1\)\(4\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)\(1\)\(4\)\(4\)\(1\)\(3\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)\(0\)\(7\)\(6\)\(0\)\(6\)\(1\)\(0\)\(1\)
Plus space\(+\)\(50\)\(3\)\(47\)\(43\)\(3\)\(40\)\(7\)\(0\)\(7\)
Minus space\(-\)\(54\)\(6\)\(48\)\(46\)\(6\)\(40\)\(8\)\(0\)\(8\)

Trace form

\( 9 q - 3 q^{2} + q^{3} + 9 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 9 q^{9} - 2 q^{10} + q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} + 9 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - 2 q^{20} + q^{21}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(462))\) 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 3 7 11
462.2.a.a 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.a \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
462.2.a.b 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.b \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.c 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.c \(-1\) \(-1\) \(2\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.d 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.d \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.e 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.e \(1\) \(-1\) \(-4\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{7}+\cdots\)
462.2.a.f 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.f \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
462.2.a.g 462.a 1.a $1$ $3.689$ \(\Q\) None 462.2.a.g \(1\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.h 462.a 1.a $2$ $3.689$ \(\Q(\sqrt{3}) \) None 462.2.a.h \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(462))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(462)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)