Properties

Label 1849.2.a
Level $1849$
Weight $2$
Character orbit 1849.a
Rep. character $\chi_{1849}(1,\cdot)$
Character field $\Q$
Dimension $130$
Newform subspaces $18$
Sturm bound $315$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(315\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1849))\).

Total New Old
Modular forms 179 171 8
Cusp forms 136 130 6
Eisenstein series 43 41 2

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

\(43\)Dim
\(+\)\(60\)
\(-\)\(70\)

Trace form

\( 130 q + 2 q^{2} + 2 q^{3} + 110 q^{4} + 4 q^{7} + 92 q^{9} + O(q^{10}) \) \( 130 q + 2 q^{2} + 2 q^{3} + 110 q^{4} + 4 q^{7} + 92 q^{9} - 4 q^{10} + 4 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{15} + 82 q^{16} - 6 q^{17} + 2 q^{18} + 6 q^{19} + 8 q^{20} + 4 q^{21} - 2 q^{22} - 8 q^{24} + 36 q^{25} - 18 q^{26} - 4 q^{27} + 6 q^{29} + 24 q^{30} + 8 q^{31} - 8 q^{32} + 14 q^{33} - 14 q^{34} + 12 q^{35} + 26 q^{36} + 4 q^{38} - 2 q^{39} - 8 q^{40} - 2 q^{41} - 8 q^{42} - 44 q^{44} + 8 q^{45} + 14 q^{46} - 12 q^{47} - 8 q^{48} + 16 q^{49} + 38 q^{50} + 2 q^{51} + 14 q^{52} - 16 q^{53} + 6 q^{54} + 24 q^{55} + 22 q^{56} - 12 q^{57} - 24 q^{58} + 20 q^{59} - 2 q^{60} - 10 q^{61} - 2 q^{62} - 4 q^{63} - 22 q^{64} - 16 q^{65} - 2 q^{66} + 2 q^{67} + 10 q^{68} - 18 q^{69} - 16 q^{70} + 10 q^{71} + 22 q^{73} + 38 q^{74} + 6 q^{75} + 4 q^{76} - 12 q^{77} + 24 q^{78} + 8 q^{79} - 14 q^{81} + 18 q^{82} - 32 q^{83} + 14 q^{84} - 24 q^{85} - 32 q^{87} + 16 q^{88} + 16 q^{89} - 86 q^{90} - 4 q^{91} + 6 q^{92} - 2 q^{93} + 8 q^{94} + 2 q^{95} + 30 q^{96} + 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 43
1849.2.a.a 1849.a 1.a $1$ $14.764$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
1849.2.a.b 1849.a 1.a $1$ $14.764$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-3q^{9}-q^{11}+3q^{13}+4q^{16}+\cdots\)
1849.2.a.c 1849.a 1.a $1$ $14.764$ \(\Q\) None \(1\) \(1\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
1849.2.a.d 1849.a 1.a $1$ $14.764$ \(\Q\) None \(2\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+4q^{5}+4q^{6}+\cdots\)
1849.2.a.e 1849.a 1.a $2$ $14.764$ \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
1849.2.a.f 1849.a 1.a $2$ $14.764$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(-2-\beta )q^{5}-2q^{6}+\cdots\)
1849.2.a.g 1849.a 1.a $2$ $14.764$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+4q^{4}-\beta q^{5}-6q^{6}+\cdots\)
1849.2.a.h 1849.a 1.a $2$ $14.764$ \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2-\beta )q^{3}+3\beta q^{4}+2\beta q^{5}+\cdots\)
1849.2.a.i 1849.a 1.a $3$ $14.764$ \(\Q(\zeta_{14})^+\) None \(-2\) \(-5\) \(-6\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
1849.2.a.j 1849.a 1.a $3$ $14.764$ \(\Q(\zeta_{14})^+\) None \(-1\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1849.2.a.k 1849.a 1.a $3$ $14.764$ \(\Q(\zeta_{14})^+\) None \(1\) \(1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1849.2.a.l 1849.a 1.a $3$ $14.764$ \(\Q(\zeta_{14})^+\) None \(2\) \(5\) \(6\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
1849.2.a.m 1849.a 1.a $10$ $14.764$ \(\Q(\zeta_{44})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1849.2.a.n 1849.a 1.a $18$ $14.764$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-5\) \(-5\) \(-11\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
1849.2.a.o 1849.a 1.a $18$ $14.764$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(5\) \(5\) \(11\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)
1849.2.a.p 1849.a 1.a $20$ $14.764$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-5\) \(1\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
1849.2.a.q 1849.a 1.a $20$ $14.764$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{19})q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots\)
1849.2.a.r 1849.a 1.a $20$ $14.764$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(-1\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1849))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1849)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)