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.

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9 q - 3 q^{2} + q^{3} + 9 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 9 q^{9} + O(q^{10}) \) \( 9 q - 3 q^{2} + q^{3} + 9 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 9 q^{9} - 2 q^{10} + q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} + 9 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - 2 q^{20} + q^{21} - 3 q^{22} - 16 q^{23} + q^{24} + 7 q^{25} - 18 q^{26} + q^{27} + q^{28} - 26 q^{29} + 6 q^{30} + 24 q^{31} - 3 q^{32} + q^{33} - 6 q^{34} - 10 q^{35} + 9 q^{36} + 6 q^{37} - 4 q^{38} + 14 q^{39} - 2 q^{40} - 14 q^{41} - 3 q^{42} + 4 q^{43} + q^{44} - 2 q^{45} + 8 q^{47} + q^{48} + 9 q^{49} + 3 q^{50} + 10 q^{51} + 6 q^{52} - 2 q^{53} + q^{54} + 6 q^{55} + q^{56} + 20 q^{57} - 2 q^{58} - 4 q^{59} + 6 q^{60} - 10 q^{61} + q^{63} + 9 q^{64} + 20 q^{65} + q^{66} + 20 q^{67} - 6 q^{68} + 8 q^{69} - 2 q^{70} - 16 q^{71} - 3 q^{72} - 14 q^{73} - 18 q^{74} - q^{75} + 4 q^{76} + q^{77} - 2 q^{78} - 48 q^{79} - 2 q^{80} + 9 q^{81} + 18 q^{82} - 12 q^{83} + q^{84} + 12 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} - 38 q^{89} - 2 q^{90} - 2 q^{91} - 16 q^{92} - 8 q^{93} - 24 q^{95} + q^{96} - 14 q^{97} - 3 q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(462))\) into newform subspaces

Label Char Prim Dim $A$ Field CM 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 \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
462.2.a.b 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.c 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.d 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.e 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(-1\) \(-4\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{7}+\cdots\)
462.2.a.f 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
462.2.a.g 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.h 462.a 1.a $2$ $3.689$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)

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

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