Properties

Label 980.2.a
Level $980$
Weight $2$
Character orbit 980.a
Rep. character $\chi_{980}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $11$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(336\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(980))\).

Total New Old
Modular forms 192 13 179
Cusp forms 145 13 132
Eisenstein series 47 0 47

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

\(2\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(4\)
Minus space\(-\)\(9\)

Trace form

\( 13q - 2q^{3} + q^{5} + 9q^{9} + O(q^{10}) \) \( 13q - 2q^{3} + q^{5} + 9q^{9} + 2q^{13} - 2q^{15} + 10q^{17} - 4q^{19} - 6q^{23} + 13q^{25} - 8q^{27} + 10q^{29} + 12q^{33} + 34q^{37} + 44q^{39} - 2q^{41} + 34q^{43} + 9q^{45} + 10q^{47} - 4q^{51} - 6q^{53} - 8q^{55} - 8q^{57} - 16q^{59} - 2q^{61} - 2q^{65} + 14q^{67} + 4q^{71} - 18q^{73} - 2q^{75} + 17q^{81} + 10q^{83} - 10q^{85} + 48q^{87} - 10q^{89} + 32q^{93} + 4q^{95} - 6q^{97} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(980))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
980.2.a.a \(1\) \(7.825\) \(\Q\) None \(0\) \(-3\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}-q^{5}+6q^{9}-2q^{11}-6q^{13}+\cdots\)
980.2.a.b \(1\) \(7.825\) \(\Q\) None \(0\) \(-3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-3q^{3}+q^{5}+6q^{9}-5q^{11}+3q^{13}+\cdots\)
980.2.a.c \(1\) \(7.825\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
980.2.a.d \(1\) \(7.825\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{9}-q^{11}+5q^{13}+\cdots\)
980.2.a.e \(1\) \(7.825\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{9}+6q^{11}-2q^{13}+\cdots\)
980.2.a.f \(1\) \(7.825\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{9}-q^{11}-5q^{13}+\cdots\)
980.2.a.g \(1\) \(7.825\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-2q^{9}+6q^{11}+2q^{13}+\cdots\)
980.2.a.h \(1\) \(7.825\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
980.2.a.i \(1\) \(7.825\) \(\Q\) None \(0\) \(3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+q^{5}+6q^{9}-2q^{11}+6q^{13}+\cdots\)
980.2.a.j \(2\) \(7.825\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-1+\cdots)q^{11}+\cdots\)
980.2.a.k \(2\) \(7.825\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(980))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(980)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)