Properties

Label 845.6.a
Level $845$
Weight $6$
Character orbit 845.a
Rep. character $\chi_{845}(1,\cdot)$
Character field $\Q$
Dimension $259$
Newform subspaces $20$
Sturm bound $546$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 845.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(546\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(845))\).

Total New Old
Modular forms 468 259 209
Cusp forms 440 259 181
Eisenstein series 28 0 28

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

\(5\)\(13\)FrickeDim
\(+\)\(+\)$+$\(61\)
\(+\)\(-\)$-$\(68\)
\(-\)\(+\)$-$\(68\)
\(-\)\(-\)$+$\(62\)
Plus space\(+\)\(123\)
Minus space\(-\)\(136\)

Trace form

\( 259 q + 2 q^{2} - 40 q^{3} + 4164 q^{4} + 25 q^{5} - 236 q^{6} + 4 q^{7} + 732 q^{8} + 20775 q^{9} + O(q^{10}) \) \( 259 q + 2 q^{2} - 40 q^{3} + 4164 q^{4} + 25 q^{5} - 236 q^{6} + 4 q^{7} + 732 q^{8} + 20775 q^{9} - 150 q^{10} - 144 q^{11} - 44 q^{12} - 328 q^{14} + 1000 q^{15} + 70536 q^{16} - 378 q^{17} - 3386 q^{18} - 1916 q^{19} + 3100 q^{20} + 9796 q^{21} - 7520 q^{22} - 3720 q^{23} - 15112 q^{24} + 161875 q^{25} - 10108 q^{27} - 6972 q^{28} - 1450 q^{29} + 7800 q^{30} + 3060 q^{31} + 28856 q^{32} + 28140 q^{33} + 30968 q^{34} - 7900 q^{35} + 296096 q^{36} - 28910 q^{37} + 28968 q^{38} - 12600 q^{40} - 34854 q^{41} + 73216 q^{42} + 7212 q^{43} + 77620 q^{44} + 125 q^{45} - 940 q^{46} + 69212 q^{47} - 35988 q^{48} + 558779 q^{49} + 1250 q^{50} + 70308 q^{51} - 90778 q^{53} + 6804 q^{54} + 3700 q^{55} + 143644 q^{56} + 75356 q^{57} + 160992 q^{58} + 48340 q^{59} + 73200 q^{60} - 62590 q^{61} - 234312 q^{62} - 80084 q^{63} + 1226092 q^{64} + 16396 q^{66} + 59064 q^{67} + 5544 q^{68} - 14700 q^{69} - 56600 q^{70} + 100544 q^{71} - 190824 q^{72} + 130646 q^{73} - 40432 q^{74} - 25000 q^{75} - 195240 q^{76} - 6788 q^{77} - 52500 q^{79} + 73200 q^{80} + 1586403 q^{81} + 252588 q^{82} - 134560 q^{83} + 330996 q^{84} - 59650 q^{85} - 4840 q^{86} - 59540 q^{87} + 230116 q^{88} + 109198 q^{89} - 21050 q^{90} + 208852 q^{92} - 175780 q^{93} - 232656 q^{94} - 102300 q^{95} - 135068 q^{96} - 269502 q^{97} - 70166 q^{98} - 359452 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(845))\) 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 13
845.6.a.a 845.a 1.a $1$ $135.524$ \(\Q\) None \(-5\) \(6\) \(25\) \(244\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{2}+6q^{3}-7q^{4}+5^{2}q^{5}-30q^{6}+\cdots\)
845.6.a.b 845.a 1.a $1$ $135.524$ \(\Q\) None \(-2\) \(-4\) \(-25\) \(-192\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-4q^{3}-28q^{4}-5^{2}q^{5}+8q^{6}+\cdots\)
845.6.a.c 845.a 1.a $3$ $135.524$ 3.3.49857.1 None \(2\) \(-16\) \(-75\) \(208\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-5-\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
845.6.a.d 845.a 1.a $4$ $135.524$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-7\) \(24\) \(-100\) \(98\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{2}-\beta _{3})q^{2}+(6+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
845.6.a.e 845.a 1.a $4$ $135.524$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(7\) \(24\) \(100\) \(-98\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{2}+\beta _{3})q^{2}+(6+\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
845.6.a.f 845.a 1.a $4$ $135.524$ 4.4.1878612.1 None \(9\) \(-4\) \(100\) \(136\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2}-\beta _{3})q^{3}+\cdots\)
845.6.a.g 845.a 1.a $6$ $135.524$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-2\) \(20\) \(-150\) \(-172\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3-\beta _{2})q^{3}+(23-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.6.a.h 845.a 1.a $6$ $135.524$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(38\) \(150\) \(-220\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{2})q^{3}+(22+\beta _{2}+\cdots)q^{4}+\cdots\)
845.6.a.i 845.a 1.a $7$ $135.524$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-11\) \(-42\) \(175\) \(-40\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}+\beta _{5})q^{3}+\cdots\)
845.6.a.j 845.a 1.a $7$ $135.524$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(11\) \(-42\) \(-175\) \(40\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(-6-\beta _{1}+\beta _{5})q^{3}+\cdots\)
845.6.a.k 845.a 1.a $12$ $135.524$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-2\) \(-300\) \(-98\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(14+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
845.6.a.l 845.a 1.a $12$ $135.524$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(20\) \(-300\) \(-236\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(20+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.6.a.m 845.a 1.a $12$ $135.524$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-2\) \(300\) \(98\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(14+\beta _{2})q^{4}+5^{2}q^{5}+\cdots\)
845.6.a.n 845.a 1.a $12$ $135.524$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(20\) \(300\) \(236\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(20+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
845.6.a.o 845.a 1.a $24$ $135.524$ None \(-8\) \(-18\) \(600\) \(-450\) $-$ $-$ $\mathrm{SU}(2)$
845.6.a.p 845.a 1.a $24$ $135.524$ None \(8\) \(-18\) \(-600\) \(450\) $+$ $-$ $\mathrm{SU}(2)$
845.6.a.q 845.a 1.a $27$ $135.524$ None \(-14\) \(-65\) \(675\) \(-325\) $-$ $-$ $\mathrm{SU}(2)$
845.6.a.r 845.a 1.a $27$ $135.524$ None \(14\) \(-65\) \(-675\) \(325\) $+$ $+$ $\mathrm{SU}(2)$
845.6.a.s 845.a 1.a $33$ $135.524$ None \(-12\) \(43\) \(-825\) \(-263\) $+$ $-$ $\mathrm{SU}(2)$
845.6.a.t 845.a 1.a $33$ $135.524$ None \(12\) \(43\) \(825\) \(263\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(845))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(845)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)