Properties

Label 841.2.a
Level $841$
Weight $2$
Character orbit 841.a
Rep. character $\chi_{841}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $11$
Sturm bound $145$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(145\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(841))\).

Total New Old
Modular forms 87 81 6
Cusp forms 58 54 4
Eisenstein series 29 27 2

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

\(29\)Dim
\(+\)\(24\)
\(-\)\(30\)

Trace form

\( 54 q + 2 q^{2} - 2 q^{3} + 40 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} + 28 q^{9} + O(q^{10}) \) \( 54 q + 2 q^{2} - 2 q^{3} + 40 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} + 28 q^{9} - 2 q^{10} - 2 q^{11} - 10 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} + 4 q^{22} + 4 q^{23} + 16 q^{24} + 8 q^{25} - 10 q^{26} - 2 q^{27} + 22 q^{28} - 28 q^{30} - 6 q^{31} - 6 q^{32} + 8 q^{33} + 10 q^{34} - 30 q^{36} + 8 q^{37} + 18 q^{38} + 10 q^{39} - 6 q^{40} - 8 q^{41} - 10 q^{42} - 10 q^{43} + 6 q^{44} + 6 q^{45} + 12 q^{46} - 2 q^{47} - 6 q^{48} - 30 q^{49} - 8 q^{50} + 24 q^{52} + 2 q^{53} + 4 q^{54} + 2 q^{55} - 8 q^{56} - 8 q^{57} - 30 q^{59} + 10 q^{60} + 4 q^{61} - 28 q^{62} + 20 q^{63} - 22 q^{64} + 4 q^{65} - 2 q^{66} + 2 q^{67} - 12 q^{68} - 12 q^{69} + 8 q^{70} + 16 q^{71} + 8 q^{72} - 8 q^{73} - 6 q^{74} + 8 q^{75} - 12 q^{76} - 8 q^{77} - 10 q^{78} + 2 q^{79} + 16 q^{80} - 50 q^{81} - 6 q^{82} - 2 q^{83} + 24 q^{84} - 4 q^{85} + 16 q^{86} - 14 q^{88} + 8 q^{89} - 8 q^{90} - 4 q^{91} - 18 q^{92} - 16 q^{93} - 2 q^{94} + 12 q^{95} - 74 q^{96} + 8 q^{97} + 2 q^{98} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(841))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
841.2.a.a 841.a 1.a $2$ $6.715$ \(\Q(\sqrt{5}) \) None 841.2.a.a \(-1\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots\)
841.2.a.b 841.a 1.a $2$ $6.715$ \(\Q(\sqrt{5}) \) None 29.2.b.a \(0\) \(0\) \(6\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+\beta q^{3}+3q^{4}+3q^{5}-5q^{6}+\cdots\)
841.2.a.c 841.a 1.a $2$ $6.715$ \(\Q(\sqrt{5}) \) None 841.2.a.a \(1\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(-1+\beta )q^{4}+(2-3\beta )q^{5}+\cdots\)
841.2.a.d 841.a 1.a $2$ $6.715$ \(\Q(\sqrt{2}) \) None 29.2.a.a \(2\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
841.2.a.e 841.a 1.a $3$ $6.715$ \(\Q(\zeta_{14})^+\) None 29.2.d.a \(-1\) \(1\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
841.2.a.f 841.a 1.a $3$ $6.715$ \(\Q(\zeta_{14})^+\) None 29.2.d.a \(1\) \(-1\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
841.2.a.g 841.a 1.a $6$ $6.715$ 6.6.11973625.1 None 841.2.a.g \(-2\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
841.2.a.h 841.a 1.a $6$ $6.715$ 6.6.11973625.1 None 841.2.a.g \(2\) \(2\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
841.2.a.i 841.a 1.a $8$ $6.715$ 8.8.2841328125.1 None 841.2.a.i \(-4\) \(-6\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
841.2.a.j 841.a 1.a $8$ $6.715$ 8.8.2841328125.1 None 841.2.a.i \(4\) \(6\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
841.2.a.k 841.a 1.a $12$ $6.715$ 12.12.\(\cdots\).1 None 29.2.e.a \(0\) \(0\) \(8\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{11}q^{2}+(-\beta _{6}-\beta _{9})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(841))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(841)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)