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

\( 6q + 4q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 6q + 4q^{3} - 4q^{7} + 2q^{9} - 4q^{15} + 12q^{17} + 8q^{19} - 4q^{21} + 6q^{25} + 16q^{27} + 2q^{29} - 2q^{31} + 2q^{35} - 20q^{37} - 4q^{39} - 2q^{41} - 12q^{47} - 8q^{49} + 4q^{51} - 4q^{53} + 2q^{59} - 20q^{61} + 20q^{63} - 4q^{65} - 12q^{67} + 42q^{71} - 4q^{73} + 4q^{75} + 28q^{77} - 12q^{79} + 6q^{81} - 4q^{83} - 10q^{85} + 4q^{87} - 12q^{89} - 20q^{91} - 20q^{93} + 8q^{95} - 8q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(460))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 23
460.2.a.a \(1\) \(3.673\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
460.2.a.b \(1\) \(3.673\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
460.2.a.c \(1\) \(3.673\) \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
460.2.a.d \(1\) \(3.673\) \(\Q\) None \(0\) \(3\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
460.2.a.e \(2\) \(3.673\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)

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

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