Properties

Label 574.2.a
Level 574
Weight 2
Character orbit a
Rep. character \(\chi_{574}(1,\cdot)\)
Character field \(\Q\)
Dimension 19
Newforms 13
Sturm bound 168
Trace bound 5

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Defining parameters

Level: \( N \) = \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 574.a (trivial)
Character field: \(\Q\)
Newforms: \( 13 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(574))\).

Total New Old
Modular forms 88 19 69
Cusp forms 81 19 62
Eisenstein series 7 0 7

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

\(2\)\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(13\)

Trace form

\( 19q - q^{2} + 4q^{3} + 19q^{4} + 2q^{5} - 4q^{6} - q^{7} - q^{8} + 23q^{9} + O(q^{10}) \) \( 19q - q^{2} + 4q^{3} + 19q^{4} + 2q^{5} - 4q^{6} - q^{7} - q^{8} + 23q^{9} - 6q^{10} + 4q^{12} - 14q^{13} + 3q^{14} + 8q^{15} + 19q^{16} - 10q^{17} - 5q^{18} - 12q^{19} + 2q^{20} + 4q^{21} - 8q^{22} + 8q^{23} - 4q^{24} + 13q^{25} - 6q^{26} - 8q^{27} - q^{28} - 2q^{29} + 16q^{30} + 24q^{31} - q^{32} - 8q^{33} - 2q^{34} - 2q^{35} + 23q^{36} + 2q^{37} + 12q^{38} - 16q^{39} - 6q^{40} - q^{41} - 4q^{42} - 36q^{43} + 26q^{45} - 8q^{46} + 16q^{47} + 4q^{48} + 19q^{49} - 23q^{50} - 8q^{51} - 14q^{52} - 10q^{53} + 8q^{54} + 24q^{55} + 3q^{56} + 24q^{57} - 18q^{58} + 4q^{59} + 8q^{60} - 6q^{61} - 5q^{63} + 19q^{64} + 68q^{65} + 16q^{67} - 10q^{68} + 8q^{69} - 2q^{70} + 32q^{71} - 5q^{72} - 34q^{73} + 10q^{74} + 4q^{75} - 12q^{76} + 4q^{77} - 16q^{79} + 2q^{80} + 35q^{81} - q^{82} - 20q^{83} + 4q^{84} - 4q^{85} - 12q^{86} - 32q^{87} - 8q^{88} + 86q^{89} - 46q^{90} + 10q^{91} + 8q^{92} - 40q^{93} + 8q^{94} - 40q^{95} - 4q^{96} - 18q^{97} - q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 41
574.2.a.a \(1\) \(4.583\) \(\Q\) None \(-1\) \(-2\) \(4\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{7}+\cdots\)
574.2.a.b \(1\) \(4.583\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
574.2.a.c \(1\) \(4.583\) \(\Q\) None \(-1\) \(1\) \(-3\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.d \(1\) \(4.583\) \(\Q\) None \(-1\) \(2\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{7}+\cdots\)
574.2.a.e \(1\) \(4.583\) \(\Q\) None \(-1\) \(2\) \(2\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots\)
574.2.a.f \(1\) \(4.583\) \(\Q\) None \(-1\) \(3\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.g \(1\) \(4.583\) \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.h \(1\) \(4.583\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
574.2.a.i \(1\) \(4.583\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.j \(1\) \(4.583\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
574.2.a.k \(2\) \(4.583\) \(\Q(\sqrt{3}) \) None \(2\) \(4\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+(1+\beta )q^{5}+2q^{6}+\cdots\)
574.2.a.l \(3\) \(4.583\) 3.3.568.1 None \(3\) \(1\) \(1\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
574.2.a.m \(4\) \(4.583\) 4.4.11348.1 None \(-4\) \(-1\) \(3\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(574))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(574)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 2}\)