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Properties

Label 8027.2.a
Level $8027$
Weight $2$
Character orbit 8027.a
Rep. character $\chi_{8027}(1,\cdot)$
Character field $\Q$
Dimension $639$
Newform subspaces $6$
Sturm bound $1400$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(1400\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8027))\).

Total New Old
Modular forms 702 639 63
Cusp forms 699 639 60
Eisenstein series 3 0 3

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

\(23\)\(349\)FrickeDim
\(+\)\(+\)$+$\(149\)
\(+\)\(-\)$-$\(170\)
\(-\)\(+\)$-$\(177\)
\(-\)\(-\)$+$\(143\)
Plus space\(+\)\(292\)
Minus space\(-\)\(347\)

Trace form

\( 639 q + q^{2} + 645 q^{4} + 6 q^{5} + 4 q^{6} + 9 q^{8} + 631 q^{9} + O(q^{10}) \) \( 639 q + q^{2} + 645 q^{4} + 6 q^{5} + 4 q^{6} + 9 q^{8} + 631 q^{9} - 6 q^{10} - 20 q^{12} + 10 q^{13} - 20 q^{14} - 4 q^{15} + 637 q^{16} - 14 q^{17} - 19 q^{18} + 8 q^{19} - 2 q^{20} + 12 q^{21} - 8 q^{22} + q^{23} - 12 q^{24} + 645 q^{25} + 26 q^{26} + 12 q^{27} + 32 q^{28} + 14 q^{29} - 12 q^{30} + 24 q^{31} - 31 q^{32} - 36 q^{33} + 6 q^{34} + 629 q^{36} + 38 q^{37} - 20 q^{39} + 18 q^{40} + 10 q^{41} - 16 q^{42} - 4 q^{43} - 40 q^{44} + 26 q^{45} - q^{46} - 12 q^{47} - 48 q^{48} + 655 q^{49} + 31 q^{50} - 60 q^{51} + 50 q^{52} - 14 q^{53} - 56 q^{54} - 36 q^{55} - 48 q^{56} + 8 q^{57} + 54 q^{58} - 52 q^{59} - 60 q^{60} + 34 q^{61} - 8 q^{62} - 68 q^{63} + 701 q^{64} + 28 q^{65} + 8 q^{66} + 24 q^{67} + 6 q^{68} + 4 q^{69} + 88 q^{70} - 92 q^{71} - 15 q^{72} + 2 q^{73} + 2 q^{74} - 96 q^{75} + 64 q^{76} + 24 q^{77} + 20 q^{78} + 24 q^{79} + 22 q^{80} + 647 q^{81} + 42 q^{82} - 12 q^{83} - 52 q^{84} + 56 q^{85} + 32 q^{86} - 44 q^{87} - 60 q^{88} + 18 q^{89} + 34 q^{90} + 40 q^{91} + 7 q^{92} + 108 q^{93} + 64 q^{94} + 8 q^{95} + 4 q^{96} + 2 q^{97} - 15 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23 349
8027.2.a.a 8027.a 1.a $1$ $64.096$ \(\Q\) None \(-2\) \(-3\) \(0\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}+6q^{6}-q^{7}+\cdots\)
8027.2.a.b 8027.a 1.a $1$ $64.096$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)
8027.2.a.c 8027.a 1.a $143$ $64.096$ None \(-17\) \(-17\) \(-22\) \(-33\) $-$ $-$ $\mathrm{SU}(2)$
8027.2.a.d 8027.a 1.a $149$ $64.096$ None \(-5\) \(-5\) \(-28\) \(-33\) $+$ $+$ $\mathrm{SU}(2)$
8027.2.a.e 8027.a 1.a $169$ $64.096$ None \(6\) \(2\) \(28\) \(38\) $+$ $-$ $\mathrm{SU}(2)$
8027.2.a.f 8027.a 1.a $176$ $64.096$ None \(19\) \(22\) \(28\) \(30\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(349))\)\(^{\oplus 2}\)