Properties

Label 1862.2.a
Level $1862$
Weight $2$
Character orbit 1862.a
Rep. character $\chi_{1862}(1,\cdot)$
Character field $\Q$
Dimension $61$
Newform subspaces $24$
Sturm bound $560$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1862.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(560\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1862))\).

Total New Old
Modular forms 296 61 235
Cusp forms 265 61 204
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.

\(2\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(23\)
Minus space\(-\)\(38\)

Trace form

\( 61q - q^{2} - 4q^{3} + 61q^{4} - 2q^{5} + 6q^{6} - q^{8} + 67q^{9} + O(q^{10}) \) \( 61q - q^{2} - 4q^{3} + 61q^{4} - 2q^{5} + 6q^{6} - q^{8} + 67q^{9} - 2q^{10} + 4q^{11} - 4q^{12} - 10q^{13} + 4q^{15} + 61q^{16} + 3q^{18} + q^{19} - 2q^{20} + 4q^{22} + 6q^{23} + 6q^{24} + 47q^{25} + 8q^{26} + 8q^{27} + 14q^{29} + 12q^{30} - 20q^{31} - q^{32} + 32q^{33} - 18q^{34} + 67q^{36} - 14q^{37} + 3q^{38} + 34q^{39} - 2q^{40} + 22q^{41} + 4q^{43} + 4q^{44} + 10q^{45} + 12q^{46} + 16q^{47} - 4q^{48} - 39q^{50} + 56q^{51} - 10q^{52} - 10q^{53} + 30q^{54} + 40q^{55} - 2q^{57} - 20q^{58} - 4q^{59} + 4q^{60} + 2q^{61} + 28q^{62} + 61q^{64} + 16q^{65} + 20q^{66} + 4q^{67} + 28q^{69} + 12q^{71} + 3q^{72} - 12q^{73} - 38q^{74} + 12q^{75} + q^{76} + 20q^{78} + 12q^{79} - 2q^{80} + 85q^{81} + 6q^{82} + 16q^{83} - 8q^{85} + 32q^{86} + 18q^{87} + 4q^{88} - 22q^{89} - 14q^{90} + 6q^{92} + 4q^{93} - 16q^{94} + 2q^{95} + 6q^{96} - 30q^{97} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 19
1862.2.a.a \(1\) \(14.868\) \(\Q\) None \(-1\) \(-2\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{8}+\cdots\)
1862.2.a.b \(1\) \(14.868\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
1862.2.a.c \(1\) \(14.868\) \(\Q\) None \(-1\) \(2\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{8}+\cdots\)
1862.2.a.d \(1\) \(14.868\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
1862.2.a.e \(1\) \(14.868\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
1862.2.a.f \(1\) \(14.868\) \(\Q\) None \(1\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
1862.2.a.g \(2\) \(14.868\) \(\Q(\sqrt{5}) \) None \(-2\) \(-3\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+3\beta )q^{5}+\cdots\)
1862.2.a.h \(2\) \(14.868\) \(\Q(\sqrt{29}) \) None \(-2\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
1862.2.a.i \(2\) \(14.868\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
1862.2.a.j \(2\) \(14.868\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
1862.2.a.k \(2\) \(14.868\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1862.2.a.l \(2\) \(14.868\) \(\Q(\sqrt{13}) \) None \(2\) \(-1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
1862.2.a.m \(2\) \(14.868\) \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\)
1862.2.a.n \(3\) \(14.868\) 3.3.257.1 None \(-3\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
1862.2.a.o \(3\) \(14.868\) 3.3.469.1 None \(-3\) \(-1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
1862.2.a.p \(3\) \(14.868\) 3.3.469.1 None \(-3\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1862.2.a.q \(3\) \(14.868\) 3.3.257.1 None \(-3\) \(2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
1862.2.a.r \(3\) \(14.868\) 3.3.469.1 None \(3\) \(1\) \(-5\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
1862.2.a.s \(4\) \(14.868\) 4.4.9792.1 None \(-4\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
1862.2.a.t \(4\) \(14.868\) 4.4.9792.1 None \(-4\) \(2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1862.2.a.u \(4\) \(14.868\) 4.4.2624.1 None \(4\) \(-6\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+(-2+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1862.2.a.v \(4\) \(14.868\) 4.4.2624.1 None \(4\) \(6\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1862.2.a.w \(5\) \(14.868\) 5.5.6530556.1 None \(5\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1862.2.a.x \(5\) \(14.868\) 5.5.6530556.1 None \(5\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1862))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1862)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 2}\)