Properties

Label 490.2.a
Level 490
Weight 2
Character orbit a
Rep. character \(\chi_{490}(1,\cdot)\)
Character field \(\Q\)
Dimension 15
Newform subspaces 13
Sturm bound 168
Trace bound 11

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Defining parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 490.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(168\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(490))\).

Total New Old
Modular forms 100 15 85
Cusp forms 69 15 54
Eisenstein series 31 0 31

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.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(5\)
Minus space\(-\)\(10\)

Trace form

\( 15q - q^{2} + 15q^{4} + q^{5} - q^{8} + 23q^{9} + O(q^{10}) \) \( 15q - q^{2} + 15q^{4} + q^{5} - q^{8} + 23q^{9} + q^{10} + 6q^{13} + 4q^{15} + 15q^{16} - 2q^{17} + 3q^{18} + q^{20} - 4q^{22} + 15q^{25} + 6q^{26} - 2q^{29} - 8q^{31} - q^{32} - 2q^{34} + 23q^{36} - 46q^{37} - 48q^{39} + q^{40} - 2q^{41} - 52q^{43} - 3q^{45} + 8q^{46} - 8q^{47} - q^{50} + 32q^{51} + 6q^{52} + 18q^{53} + 4q^{55} - 40q^{57} + 2q^{58} + 8q^{59} + 4q^{60} + 14q^{61} - 8q^{62} + 15q^{64} - 2q^{65} - 36q^{67} - 2q^{68} + 40q^{71} + 3q^{72} - 2q^{73} + 14q^{74} + 24q^{78} - 32q^{79} + q^{80} + 55q^{81} - 2q^{82} - 8q^{83} + 14q^{85} + 16q^{86} - 4q^{88} - 10q^{89} - 3q^{90} - 24q^{93} - 8q^{94} + 4q^{95} - 2q^{97} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(490))\) 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
490.2.a.a \(1\) \(3.913\) \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
490.2.a.b \(1\) \(3.913\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
490.2.a.c \(1\) \(3.913\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
490.2.a.d \(1\) \(3.913\) \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots\)
490.2.a.e \(1\) \(3.913\) \(\Q\) None \(1\) \(-3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{8}+\cdots\)
490.2.a.f \(1\) \(3.913\) \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.g \(1\) \(3.913\) \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.h \(1\) \(3.913\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
490.2.a.i \(1\) \(3.913\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.j \(1\) \(3.913\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.k \(1\) \(3.913\) \(\Q\) None \(1\) \(3\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+q^{8}+\cdots\)
490.2.a.l \(2\) \(3.913\) \(\Q(\sqrt{2}) \) None \(-2\) \(-4\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
490.2.a.m \(2\) \(3.913\) \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(490))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(490)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)