Properties

Label 920.2.a
Level $920$
Weight $2$
Character orbit 920.a
Rep. character $\chi_{920}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $10$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(920))\).

Total New Old
Modular forms 152 22 130
Cusp forms 137 22 115
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.

\(2\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(6\)
Minus space\(-\)\(16\)

Trace form

\( 22q + 8q^{7} + 34q^{9} + O(q^{10}) \) \( 22q + 8q^{7} + 34q^{9} - 4q^{11} + 4q^{13} + 4q^{17} - 4q^{19} + 8q^{21} + 22q^{25} - 8q^{29} + 32q^{31} + 24q^{33} + 12q^{35} + 8q^{37} + 32q^{39} + 12q^{41} + 20q^{43} + 22q^{49} + 16q^{51} + 24q^{53} + 32q^{57} - 12q^{59} + 32q^{61} - 12q^{67} - 16q^{71} + 36q^{73} - 16q^{77} - 16q^{79} + 38q^{81} - 28q^{83} - 4q^{85} - 48q^{87} - 12q^{89} + 24q^{91} - 32q^{93} - 8q^{95} + 28q^{97} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(920))\) 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
920.2.a.a \(1\) \(7.346\) \(\Q\) None \(0\) \(-3\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q-3q^{3}+q^{5}-2q^{7}+6q^{9}+q^{13}+\cdots\)
920.2.a.b \(1\) \(7.346\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-2q^{9}+2q^{11}-5q^{13}+\cdots\)
920.2.a.c \(1\) \(7.346\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
920.2.a.d \(1\) \(7.346\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
920.2.a.e \(2\) \(7.346\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
920.2.a.f \(2\) \(7.346\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{5}+2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
920.2.a.g \(3\) \(7.346\) 3.3.621.1 None \(0\) \(0\) \(-3\) \(3\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
920.2.a.h \(3\) \(7.346\) 3.3.2597.1 None \(0\) \(1\) \(3\) \(2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
920.2.a.i \(3\) \(7.346\) 3.3.229.1 None \(0\) \(2\) \(3\) \(7\) \(+\) \(-\) \(+\) \(q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
920.2.a.j \(5\) \(7.346\) 5.5.13955077.1 None \(0\) \(0\) \(-5\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)