Properties

Label 1045.6.a
Level $1045$
Weight $6$
Character orbit 1045.a
Rep. character $\chi_{1045}(1,\cdot)$
Character field $\Q$
Dimension $300$
Newform subspaces $8$
Sturm bound $720$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(720\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1045))\).

Total New Old
Modular forms 604 300 304
Cusp forms 596 300 296
Eisenstein series 8 0 8

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

\(5\)\(11\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(37\)
\(+\)\(+\)\(-\)\(-\)\(39\)
\(+\)\(-\)\(+\)\(-\)\(37\)
\(+\)\(-\)\(-\)\(+\)\(35\)
\(-\)\(+\)\(+\)\(-\)\(38\)
\(-\)\(+\)\(-\)\(+\)\(36\)
\(-\)\(-\)\(+\)\(+\)\(38\)
\(-\)\(-\)\(-\)\(-\)\(40\)
Plus space\(+\)\(146\)
Minus space\(-\)\(154\)

Trace form

\( 300 q + 4800 q^{4} + 100 q^{5} + 296 q^{6} - 1704 q^{8} + 23540 q^{9} + O(q^{10}) \) \( 300 q + 4800 q^{4} + 100 q^{5} + 296 q^{6} - 1704 q^{8} + 23540 q^{9} + 1216 q^{12} - 2960 q^{14} + 76040 q^{16} - 14144 q^{18} + 1000 q^{20} + 8960 q^{21} + 12696 q^{23} - 15128 q^{24} + 187500 q^{25} + 16096 q^{26} - 14928 q^{27} - 17840 q^{29} + 15200 q^{30} + 1640 q^{31} - 62168 q^{32} - 4360 q^{34} - 6200 q^{35} + 421176 q^{36} + 17328 q^{38} - 64152 q^{39} + 34552 q^{41} + 74680 q^{42} + 49320 q^{43} + 4840 q^{44} - 11100 q^{45} + 43168 q^{46} + 61680 q^{47} + 195608 q^{48} + 713332 q^{49} - 18832 q^{51} + 183528 q^{52} - 24976 q^{53} + 231984 q^{54} + 24200 q^{55} - 70840 q^{56} - 116712 q^{58} - 24152 q^{59} - 112568 q^{61} + 408656 q^{62} - 440824 q^{63} + 1053664 q^{64} - 200 q^{65} - 175992 q^{67} + 377536 q^{68} + 248624 q^{69} - 80200 q^{70} - 163768 q^{71} - 866680 q^{72} + 7664 q^{73} - 284344 q^{74} + 35816 q^{77} + 472712 q^{78} - 98696 q^{79} + 57600 q^{80} + 2292332 q^{81} - 656672 q^{82} - 574952 q^{83} + 1087560 q^{84} + 3800 q^{85} + 454776 q^{86} + 92296 q^{87} - 169208 q^{89} - 390704 q^{91} + 748896 q^{92} + 657600 q^{93} - 401392 q^{94} + 328600 q^{96} - 61816 q^{97} + 43576 q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1045))\) 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 11 19
1045.6.a.a 1045.a 1.a $35$ $167.601$ None \(-4\) \(-27\) \(-875\) \(117\) $+$ $-$ $-$ $\mathrm{SU}(2)$
1045.6.a.b 1045.a 1.a $36$ $167.601$ None \(-8\) \(-63\) \(900\) \(-509\) $-$ $+$ $-$ $\mathrm{SU}(2)$
1045.6.a.c 1045.a 1.a $37$ $167.601$ None \(-12\) \(-27\) \(-925\) \(337\) $+$ $+$ $+$ $\mathrm{SU}(2)$
1045.6.a.d 1045.a 1.a $37$ $167.601$ None \(4\) \(27\) \(-925\) \(-79\) $+$ $-$ $+$ $\mathrm{SU}(2)$
1045.6.a.e 1045.a 1.a $38$ $167.601$ None \(-24\) \(-63\) \(950\) \(-729\) $-$ $-$ $+$ $\mathrm{SU}(2)$
1045.6.a.f 1045.a 1.a $38$ $167.601$ None \(8\) \(63\) \(950\) \(275\) $-$ $+$ $+$ $\mathrm{SU}(2)$
1045.6.a.g 1045.a 1.a $39$ $167.601$ None \(12\) \(27\) \(-975\) \(-251\) $+$ $+$ $-$ $\mathrm{SU}(2)$
1045.6.a.h 1045.a 1.a $40$ $167.601$ None \(24\) \(63\) \(1000\) \(839\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1045))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1045)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)