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Properties

Label 1859.4.a
Level $1859$
Weight $4$
Character orbit 1859.a
Rep. character $\chi_{1859}(1,\cdot)$
Character field $\Q$
Dimension $388$
Newform subspaces $17$
Sturm bound $728$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(728\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1859))\).

Total New Old
Modular forms 560 388 172
Cusp forms 532 388 144
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.

\(11\)\(13\)FrickeDim
\(+\)\(+\)$+$\(102\)
\(+\)\(-\)$-$\(93\)
\(-\)\(+\)$-$\(88\)
\(-\)\(-\)$+$\(105\)
Plus space\(+\)\(207\)
Minus space\(-\)\(181\)

Trace form

\( 388 q - 2 q^{2} - 2 q^{3} + 1544 q^{4} - 14 q^{5} + 34 q^{6} - 20 q^{7} - 72 q^{8} + 3554 q^{9} + O(q^{10}) \) \( 388 q - 2 q^{2} - 2 q^{3} + 1544 q^{4} - 14 q^{5} + 34 q^{6} - 20 q^{7} - 72 q^{8} + 3554 q^{9} + 58 q^{10} - 22 q^{11} - 244 q^{12} + 212 q^{14} - 18 q^{15} + 6320 q^{16} - 36 q^{17} - 428 q^{18} - 160 q^{19} - 160 q^{20} - 92 q^{21} + 22 q^{22} + 222 q^{23} + 732 q^{24} + 9470 q^{25} + 634 q^{27} - 100 q^{28} - 120 q^{29} - 474 q^{30} - 22 q^{31} - 508 q^{32} + 22 q^{33} - 1108 q^{34} - 308 q^{35} + 14000 q^{36} - 122 q^{37} + 1144 q^{38} + 1164 q^{40} - 8 q^{41} + 1952 q^{42} - 188 q^{43} - 528 q^{44} + 908 q^{45} + 306 q^{46} + 540 q^{47} - 76 q^{48} + 18924 q^{49} + 2660 q^{50} - 548 q^{51} - 592 q^{53} + 3978 q^{54} + 418 q^{55} + 708 q^{56} + 2344 q^{57} + 940 q^{58} - 606 q^{59} + 3700 q^{60} - 2512 q^{61} - 1234 q^{62} - 2688 q^{63} + 29068 q^{64} - 286 q^{66} + 450 q^{67} - 592 q^{68} + 2586 q^{69} + 88 q^{70} - 890 q^{71} - 1844 q^{72} + 40 q^{73} + 3214 q^{74} - 2992 q^{75} + 304 q^{76} + 396 q^{77} + 724 q^{79} + 1832 q^{80} + 29988 q^{81} - 3040 q^{82} + 1788 q^{83} + 10436 q^{84} - 340 q^{85} + 6188 q^{86} - 4424 q^{87} - 132 q^{88} - 2990 q^{89} + 732 q^{90} + 1164 q^{92} - 886 q^{93} + 72 q^{94} - 696 q^{95} - 2068 q^{96} - 2194 q^{97} - 1990 q^{98} - 484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1859))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 13
1859.4.a.a 1859.a 1.a $2$ $109.685$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(-20\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
1859.4.a.b 1859.a 1.a $4$ $109.685$ 4.4.297133.1 None \(0\) \(-4\) \(6\) \(17\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
1859.4.a.c 1859.a 1.a $6$ $109.685$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(-6\) \(8\) \(53\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.d 1859.a 1.a $9$ $109.685$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(8\) \(-30\) \(-25\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1859.4.a.e 1859.a 1.a $11$ $109.685$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-6\) \(6\) \(4\) \(-45\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.f 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-4\) \(-6\) \(-16\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.g 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(-6\) \(-24\) \(-62\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.h 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(-6\) \(24\) \(62\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
1859.4.a.i 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(4\) \(-6\) \(16\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
1859.4.a.j 1859.a 1.a $18$ $109.685$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(0\) \(-20\) \(-28\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.k 1859.a 1.a $18$ $109.685$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(20\) \(28\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)
1859.4.a.l 1859.a 1.a $36$ $109.685$ None \(-4\) \(12\) \(-40\) \(-56\) $+$ $-$ $\mathrm{SU}(2)$
1859.4.a.m 1859.a 1.a $36$ $109.685$ None \(4\) \(12\) \(40\) \(56\) $-$ $-$ $\mathrm{SU}(2)$
1859.4.a.n 1859.a 1.a $39$ $109.685$ None \(0\) \(-23\) \(-23\) \(4\) $-$ $+$ $\mathrm{SU}(2)$
1859.4.a.o 1859.a 1.a $39$ $109.685$ None \(0\) \(-23\) \(23\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$
1859.4.a.p 1859.a 1.a $51$ $109.685$ None \(0\) \(21\) \(-41\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$
1859.4.a.q 1859.a 1.a $51$ $109.685$ None \(0\) \(21\) \(41\) \(4\) $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1859))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1859)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)