Properties

Label 460.2.a
Level $460$
Weight $2$
Character orbit 460.a
Rep. character $\chi_{460}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $5$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(460))\).

Total New Old
Modular forms 78 6 72
Cusp forms 67 6 61
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.

\(2\)\(5\)\(23\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\( 6 q + 4 q^{3} - 4 q^{7} + 2 q^{9} - 4 q^{15} + 12 q^{17} + 8 q^{19} - 4 q^{21} + 6 q^{25} + 16 q^{27} + 2 q^{29} - 2 q^{31} + 2 q^{35} - 20 q^{37} - 4 q^{39} - 2 q^{41} - 12 q^{47} - 8 q^{49} + 4 q^{51}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(460))\) 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 5 23
460.2.a.a 460.a 1.a $1$ $3.673$ \(\Q\) None 460.2.a.a \(0\) \(-1\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
460.2.a.b 460.a 1.a $1$ $3.673$ \(\Q\) None 460.2.a.b \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
460.2.a.c 460.a 1.a $1$ $3.673$ \(\Q\) None 460.2.a.c \(0\) \(1\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
460.2.a.d 460.a 1.a $1$ $3.673$ \(\Q\) None 460.2.a.d \(0\) \(3\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
460.2.a.e 460.a 1.a $2$ $3.673$ \(\Q(\sqrt{17}) \) None 460.2.a.e \(0\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(460))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(460)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)