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Properties

Label 464.4.a
Level $464$
Weight $4$
Character orbit 464.a
Rep. character $\chi_{464}(1,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $14$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 464.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(464))\).

Total New Old
Modular forms 186 42 144
Cusp forms 174 42 132
Eisenstein series 12 0 12

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

\(2\)\(29\)FrickeDim
\(+\)\(+\)$+$\(12\)
\(+\)\(-\)$-$\(9\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(24\)
Minus space\(-\)\(18\)

Trace form

\( 42 q - 6 q^{3} + 36 q^{7} + 398 q^{9} + O(q^{10}) \) \( 42 q - 6 q^{3} + 36 q^{7} + 398 q^{9} - 66 q^{11} + 72 q^{15} - 76 q^{17} + 90 q^{19} - 84 q^{23} + 1050 q^{25} + 228 q^{27} - 318 q^{31} - 384 q^{33} + 576 q^{35} + 732 q^{39} + 276 q^{41} + 510 q^{43} + 1058 q^{47} + 1802 q^{49} - 44 q^{51} + 1364 q^{55} + 296 q^{57} + 748 q^{59} - 912 q^{61} + 1276 q^{63} + 184 q^{65} - 168 q^{67} + 512 q^{69} + 112 q^{71} + 1044 q^{73} + 18 q^{75} + 656 q^{77} - 1610 q^{79} + 4098 q^{81} + 2196 q^{83} + 1536 q^{85} + 522 q^{87} - 1796 q^{89} + 1936 q^{91} + 800 q^{93} + 208 q^{95} + 756 q^{97} + 874 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(464))\) 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 29
464.4.a.a 464.a 1.a $1$ $27.377$ \(\Q\) None \(0\) \(-7\) \(5\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-7q^{3}+5q^{5}+2q^{7}+22q^{9}-37q^{11}+\cdots\)
464.4.a.b 464.a 1.a $1$ $27.377$ \(\Q\) None \(0\) \(7\) \(-15\) \(18\) $-$ $+$ $\mathrm{SU}(2)$ \(q+7q^{3}-15q^{5}+18q^{7}+22q^{9}-3^{3}q^{11}+\cdots\)
464.4.a.c 464.a 1.a $2$ $27.377$ \(\Q(\sqrt{22}) \) None \(0\) \(-10\) \(30\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-5+\beta )q^{3}+15q^{5}-2\beta q^{7}+(20+\cdots)q^{9}+\cdots\)
464.4.a.d 464.a 1.a $2$ $27.377$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-10\) \(20\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-5-2\beta )q^{5}+(10+4\beta )q^{7}+\cdots\)
464.4.a.e 464.a 1.a $2$ $27.377$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(-10\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-5+6\beta )q^{5}+(8+8\beta )q^{7}+\cdots\)
464.4.a.f 464.a 1.a $2$ $27.377$ \(\Q(\sqrt{2}) \) None \(0\) \(10\) \(-10\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(5+3\beta )q^{3}+(-5+4\beta )q^{5}+(8-10\beta )q^{7}+\cdots\)
464.4.a.g 464.a 1.a $3$ $27.377$ 3.3.229.1 None \(0\) \(-6\) \(4\) \(-16\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+3\beta _{2})q^{3}+(1+3\beta _{1}-4\beta _{2})q^{5}+\cdots\)
464.4.a.h 464.a 1.a $3$ $27.377$ 3.3.4481.1 None \(0\) \(-3\) \(11\) \(38\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(4+\beta _{1}+\beta _{2})q^{5}+\cdots\)
464.4.a.i 464.a 1.a $3$ $27.377$ 3.3.19816.1 None \(0\) \(-2\) \(20\) \(-24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(6+2\beta _{1}+\beta _{2})q^{5}+\cdots\)
464.4.a.j 464.a 1.a $3$ $27.377$ 3.3.148344.1 None \(0\) \(10\) \(-20\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{3}+(-7+\beta _{2})q^{5}+(-4+\cdots)q^{7}+\cdots\)
464.4.a.k 464.a 1.a $4$ $27.377$ 4.4.225792.1 None \(0\) \(0\) \(-20\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-5-\beta _{2})q^{5}+(2-2\beta _{1}+\cdots)q^{7}+\cdots\)
464.4.a.l 464.a 1.a $5$ $27.377$ 5.5.13458092.1 None \(0\) \(-8\) \(10\) \(-40\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{3})q^{3}+(2-2\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
464.4.a.m 464.a 1.a $5$ $27.377$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-4\) \(10\) \(-32\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(2+\beta _{3})q^{5}+(-6+\cdots)q^{7}+\cdots\)
464.4.a.n 464.a 1.a $6$ $27.377$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(5\) \(-5\) \(38\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(464))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(464)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 2}\)