Properties

Label 476.2.a
Level $476$
Weight $2$
Character orbit 476.a
Rep. character $\chi_{476}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 476.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(476))\).

Total New Old
Modular forms 78 8 70
Cusp forms 67 8 59
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.

\(2\)\(7\)\(17\)FrickeDim
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(4\)

Trace form

\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} - 4 q^{19} + 8 q^{23} - 12 q^{25} - 16 q^{27} - 4 q^{29} - 4 q^{31} + 4 q^{33} - 4 q^{35} - 8 q^{37} - 4 q^{39} + 4 q^{41} - 12 q^{43} + 16 q^{45} + 16 q^{47} + 8 q^{49} + 4 q^{51} - 4 q^{53} - 4 q^{55} + 4 q^{57} - 16 q^{59} + 4 q^{61} + 8 q^{63} + 24 q^{65} - 4 q^{67} - 4 q^{69} - 8 q^{71} + 4 q^{73} + 24 q^{75} - 4 q^{79} + 8 q^{81} + 12 q^{83} - 12 q^{87} - 32 q^{89} + 4 q^{91} - 12 q^{95} - 28 q^{97} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(476))\) 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 7 17
476.2.a.a 476.a 1.a $2$ $3.801$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+\beta )q^{5}+q^{7}+\cdots\)
476.2.a.b 476.a 1.a $2$ $3.801$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
476.2.a.c 476.a 1.a $2$ $3.801$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+4q^{11}+\cdots\)
476.2.a.d 476.a 1.a $2$ $3.801$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(476))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)