Properties

Label 8045.2.a
Level $8045$
Weight $2$
Character orbit 8045.a
Rep. character $\chi_{8045}(1,\cdot)$
Character field $\Q$
Dimension $537$
Newform subspaces $5$
Sturm bound $1610$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8045 = 5 \cdot 1609 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8045.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1610\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8045))\).

Total New Old
Modular forms 806 537 269
Cusp forms 803 537 266
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.

\(5\)\(1609\)FrickeDim
\(+\)\(+\)$+$\(126\)
\(+\)\(-\)$-$\(142\)
\(-\)\(+\)$-$\(142\)
\(-\)\(-\)$+$\(127\)
Plus space\(+\)\(253\)
Minus space\(-\)\(284\)

Trace form

\( 537 q - q^{2} + 4 q^{3} + 539 q^{4} + q^{5} + 4 q^{7} - 9 q^{8} + 545 q^{9} + O(q^{10}) \) \( 537 q - q^{2} + 4 q^{3} + 539 q^{4} + q^{5} + 4 q^{7} - 9 q^{8} + 545 q^{9} + 3 q^{10} - 4 q^{11} - 4 q^{12} + 10 q^{13} + 539 q^{16} + 6 q^{17} - 29 q^{18} + 20 q^{19} + 7 q^{20} - 12 q^{22} - 12 q^{23} - 24 q^{24} + 537 q^{25} - 2 q^{26} + 4 q^{27} + 4 q^{28} + 6 q^{29} - 4 q^{30} + 24 q^{31} - 29 q^{32} + 20 q^{33} + 10 q^{34} - 4 q^{35} + 563 q^{36} + 18 q^{37} + 20 q^{38} - 12 q^{39} + 15 q^{40} + 10 q^{41} - 40 q^{42} + 8 q^{43} - 52 q^{44} + 13 q^{45} - 8 q^{46} - 24 q^{47} - 28 q^{48} + 581 q^{49} - q^{50} - 16 q^{51} - 30 q^{52} - 14 q^{53} - 72 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 66 q^{58} - 24 q^{59} - 16 q^{60} + 38 q^{61} - 72 q^{62} - 12 q^{63} + 495 q^{64} + 6 q^{65} + 12 q^{66} - 16 q^{67} + 14 q^{68} - 4 q^{69} - 4 q^{70} + 16 q^{71} - 113 q^{72} + 30 q^{73} - 62 q^{74} + 4 q^{75} + 16 q^{76} - 48 q^{77} - 36 q^{78} - 20 q^{79} + 15 q^{80} + 593 q^{81} + 10 q^{82} - 20 q^{83} - 60 q^{84} - 2 q^{85} + 12 q^{86} - 48 q^{87} - 60 q^{88} + 6 q^{89} + 39 q^{90} + 16 q^{91} - 88 q^{92} - 48 q^{93} + 8 q^{94} - 12 q^{95} - 80 q^{96} + 46 q^{97} - 69 q^{98} - 72 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8045))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 1609
8045.2.a.a 8045.a 1.a $1$ $64.240$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\)
8045.2.a.b 8045.a 1.a $126$ $64.240$ None \(5\) \(-9\) \(-126\) \(-23\) $+$ $+$ $\mathrm{SU}(2)$
8045.2.a.c 8045.a 1.a $127$ $64.240$ None \(-20\) \(-31\) \(127\) \(-63\) $-$ $-$ $\mathrm{SU}(2)$
8045.2.a.d 8045.a 1.a $141$ $64.240$ None \(-8\) \(11\) \(-141\) \(29\) $+$ $-$ $\mathrm{SU}(2)$
8045.2.a.e 8045.a 1.a $142$ $64.240$ None \(21\) \(33\) \(142\) \(63\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8045))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1609))\)\(^{\oplus 2}\)