Properties

Label 798.2.a
Level $798$
Weight $2$
Character orbit 798.a
Rep. character $\chi_{798}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $13$
Sturm bound $320$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(320\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(798))\).

Total New Old
Modular forms 168 17 151
Cusp forms 153 17 136
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.

\(2\)\(3\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(12\)

Trace form

\( 17 q - 3 q^{2} + q^{3} + 17 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 17 q^{9} + O(q^{10}) \) \( 17 q - 3 q^{2} + q^{3} + 17 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 17 q^{9} - 2 q^{10} - 4 q^{11} + q^{12} - 10 q^{13} + q^{14} + 6 q^{15} + 17 q^{16} - 6 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + q^{21} + 12 q^{22} + 8 q^{23} + q^{24} + 31 q^{25} - 10 q^{26} + q^{27} + q^{28} + 6 q^{29} - 2 q^{30} - 16 q^{31} - 3 q^{32} - 4 q^{33} - 22 q^{34} + 6 q^{35} + 17 q^{36} + 14 q^{37} + q^{38} - 2 q^{39} - 2 q^{40} - 14 q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} - 2 q^{45} + 16 q^{47} + q^{48} + 17 q^{49} + 3 q^{50} - 6 q^{51} - 10 q^{52} + 14 q^{53} + q^{54} + 56 q^{55} + q^{56} - 3 q^{57} - 2 q^{58} - 4 q^{59} + 6 q^{60} - 34 q^{61} + 16 q^{62} + q^{63} + 17 q^{64} + 36 q^{65} - 12 q^{66} + 12 q^{67} - 6 q^{68} + 8 q^{69} + 6 q^{70} + 24 q^{71} - 3 q^{72} - 6 q^{73} - 2 q^{74} - q^{75} + q^{76} + 12 q^{77} + 6 q^{78} - 32 q^{79} - 2 q^{80} + 17 q^{81} + 26 q^{82} + 36 q^{83} + q^{84} + 44 q^{85} + 12 q^{86} - 2 q^{87} + 12 q^{88} + 2 q^{89} - 2 q^{90} + 6 q^{91} + 8 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} + q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(798))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 19
798.2.a.a \(1\) \(6.372\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
798.2.a.b \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.c \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.d \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
798.2.a.e \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.f \(1\) \(6.372\) \(\Q\) None \(-1\) \(1\) \(4\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.g \(1\) \(6.372\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
798.2.a.h \(1\) \(6.372\) \(\Q\) None \(1\) \(1\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.i \(1\) \(6.372\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.j \(2\) \(6.372\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
798.2.a.k \(2\) \(6.372\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
798.2.a.l \(2\) \(6.372\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
798.2.a.m \(2\) \(6.372\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(798))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(798)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 2}\)