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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 13
1859.4.a.a \(2\) \(109.685\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(-20\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
1859.4.a.b \(4\) \(109.685\) 4.4.297133.1 None \(0\) \(-4\) \(6\) \(17\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
1859.4.a.c \(6\) \(109.685\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(-6\) \(8\) \(53\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.d \(9\) \(109.685\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(8\) \(-30\) \(-25\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1859.4.a.e \(11\) \(109.685\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-6\) \(6\) \(4\) \(-45\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.f \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-4\) \(-6\) \(-16\) \(6\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.g \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(-6\) \(-24\) \(-62\) \(-\) \(+\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.h \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(-6\) \(24\) \(62\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
1859.4.a.i \(17\) \(109.685\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(4\) \(-6\) \(16\) \(-6\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
1859.4.a.j \(18\) \(109.685\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(0\) \(-20\) \(-28\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.k \(18\) \(109.685\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(20\) \(28\) \(-\) \(-\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)
1859.4.a.l \(36\) \(109.685\) None \(-4\) \(12\) \(-40\) \(-56\) \(+\) \(-\)
1859.4.a.m \(36\) \(109.685\) None \(4\) \(12\) \(40\) \(56\) \(-\) \(-\)
1859.4.a.n \(39\) \(109.685\) None \(0\) \(-23\) \(-23\) \(4\) \(-\) \(+\)
1859.4.a.o \(39\) \(109.685\) None \(0\) \(-23\) \(23\) \(-4\) \(+\) \(-\)
1859.4.a.p \(51\) \(109.685\) None \(0\) \(21\) \(-41\) \(-4\) \(+\) \(+\)
1859.4.a.q \(51\) \(109.685\) None \(0\) \(21\) \(41\) \(4\) \(-\) \(-\)

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

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