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Properties

Label 483.4.a
Level $483$
Weight $4$
Character orbit 483.a
Rep. character $\chi_{483}(1,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $9$
Sturm bound $256$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(483))\).

Total New Old
Modular forms 196 64 132
Cusp forms 188 64 124
Eisenstein series 8 0 8

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

\(3\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(36\)
Minus space\(-\)\(28\)

Trace form

\( 64 q + 8 q^{2} + 240 q^{4} + 32 q^{5} + 96 q^{8} + 576 q^{9} - 64 q^{10} - 48 q^{12} + 288 q^{13} + 976 q^{16} - 176 q^{17} + 72 q^{18} + 416 q^{20} + 432 q^{22} + 1864 q^{25} - 144 q^{26} + 592 q^{29}+ \cdots + 392 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(483))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 23
483.4.a.a 483.a 1.a $3$ $28.498$ 3.3.3877.1 None 483.4.a.a \(-4\) \(9\) \(2\) \(-21\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+3q^{3}+(1+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.b 483.a 1.a $4$ $28.498$ 4.4.8184789.1 None 483.4.a.b \(2\) \(12\) \(-23\) \(-28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+3q^{3}+(3+\beta _{1})q^{4}+(-6+\cdots)q^{5}+\cdots\)
483.4.a.c 483.a 1.a $7$ $28.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 483.4.a.c \(-6\) \(21\) \(-41\) \(49\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
483.4.a.d 483.a 1.a $7$ $28.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 483.4.a.d \(-2\) \(-21\) \(-11\) \(-49\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{4}+\beta _{5})q^{4}+\cdots\)
483.4.a.e 483.a 1.a $7$ $28.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 483.4.a.e \(2\) \(-21\) \(-11\) \(49\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
483.4.a.f 483.a 1.a $9$ $28.498$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 483.4.a.f \(0\) \(-27\) \(29\) \(63\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(3+\beta _{7}+\cdots)q^{5}+\cdots\)
483.4.a.g 483.a 1.a $9$ $28.498$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 483.4.a.g \(4\) \(-27\) \(9\) \(-63\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
483.4.a.h 483.a 1.a $9$ $28.498$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 483.4.a.h \(4\) \(27\) \(39\) \(-63\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(4+\beta _{4}+\cdots)q^{5}+\cdots\)
483.4.a.i 483.a 1.a $9$ $28.498$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 483.4.a.i \(8\) \(27\) \(39\) \(63\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(4-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(483))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(483)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)