Properties

Label 456.2.a
Level $456$
Weight $2$
Character orbit 456.a
Rep. character $\chi_{456}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $160$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(160\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(456))\).

Total New Old
Modular forms 88 8 80
Cusp forms 73 8 65
Eisenstein series 15 0 15

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8q + 4q^{5} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 8q + 4q^{5} - 4q^{7} + 8q^{9} + 4q^{13} - 4q^{15} + 4q^{17} + 6q^{19} + 12q^{23} + 20q^{25} - 4q^{29} - 12q^{31} + 12q^{33} + 12q^{35} + 4q^{37} - 8q^{39} - 4q^{41} + 4q^{43} + 4q^{45} + 24q^{47} + 12q^{49} - 8q^{51} - 12q^{53} - 4q^{55} - 2q^{57} + 16q^{59} - 20q^{61} - 4q^{63} - 32q^{65} - 32q^{67} + 4q^{73} - 16q^{75} - 28q^{77} + 12q^{79} + 8q^{81} - 12q^{83} - 4q^{85} - 4q^{87} - 36q^{89} - 40q^{91} - 8q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(456))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
456.2.a.a \(1\) \(3.641\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
456.2.a.b \(1\) \(3.641\) \(\Q\) None \(0\) \(-1\) \(4\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
456.2.a.c \(1\) \(3.641\) \(\Q\) None \(0\) \(1\) \(-3\) \(-3\) \(+\) \(-\) \(-\) \(q+q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
456.2.a.d \(1\) \(3.641\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
456.2.a.e \(2\) \(3.641\) \(\Q(\sqrt{41}) \) None \(0\) \(-2\) \(-1\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
456.2.a.f \(2\) \(3.641\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 2}\)