Properties

Label 1849.4.a
Level $1849$
Weight $4$
Character orbit 1849.a
Rep. character $\chi_{1849}(1,\cdot)$
Character field $\Q$
Dimension $431$
Newform subspaces $13$
Sturm bound $630$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(630\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1849))\).

Total New Old
Modular forms 495 472 23
Cusp forms 451 431 20
Eisenstein series 44 41 3

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

\(43\)Dim.
\(+\)\(221\)
\(-\)\(210\)

Trace form

\( 431q - 2q^{2} + 4q^{3} + 1656q^{4} - 16q^{5} + 30q^{6} + 12q^{7} + 12q^{8} + 3519q^{9} + O(q^{10}) \) \( 431q - 2q^{2} + 4q^{3} + 1656q^{4} - 16q^{5} + 30q^{6} + 12q^{7} + 12q^{8} + 3519q^{9} - 54q^{10} + 80q^{11} + 96q^{12} - 58q^{13} + 72q^{14} + 32q^{15} + 5900q^{16} + 196q^{17} - 218q^{18} - 24q^{19} - 216q^{20} + 108q^{21} + 302q^{22} - 2q^{23} + 358q^{24} + 8921q^{25} + 6q^{26} - 20q^{27} + 484q^{28} - 416q^{29} + 96q^{30} - 318q^{31} - 216q^{32} - 508q^{33} + 54q^{34} + 176q^{35} + 12402q^{36} + 180q^{37} + 82q^{38} - 388q^{39} - 746q^{40} + 100q^{41} + 32q^{42} + 990q^{44} + 4q^{45} - 994q^{46} - 558q^{47} + 752q^{48} + 14849q^{49} - 1934q^{50} - 408q^{51} - 280q^{52} + 886q^{53} - 822q^{54} + 372q^{55} - 222q^{56} + 768q^{57} + 1826q^{58} - 1152q^{59} + 2398q^{60} + 956q^{61} - 1506q^{62} + 376q^{63} + 17916q^{64} + 412q^{65} - 1206q^{66} + 680q^{67} + 1254q^{68} + 2368q^{69} + 2620q^{70} - 324q^{71} - 252q^{72} - 1492q^{73} - 1504q^{74} + 2432q^{75} - 2676q^{76} - 616q^{77} - 2132q^{78} + 778q^{79} - 2368q^{80} + 20159q^{81} + 614q^{82} + 1868q^{83} - 2630q^{84} + 68q^{85} - 814q^{87} - 1208q^{88} - 2640q^{89} + 392q^{90} + 3048q^{91} - 558q^{92} - 1844q^{93} - 964q^{94} - 1660q^{95} + 3164q^{96} + 1340q^{97} - 4050q^{98} + 1220q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 43
1849.4.a.a \(1\) \(109.095\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(+\) \(q-8q^{4}-3^{3}q^{9}+2^{5}q^{11}-90q^{13}+\cdots\)
1849.4.a.b \(4\) \(109.095\) 4.4.45868.1 None \(4\) \(11\) \(27\) \(20\) \(-\) \(q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
1849.4.a.c \(6\) \(109.095\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(-7\) \(-43\) \(-8\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
1849.4.a.d \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(5\) \(19\) \(51\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(2-\beta _{7}+\cdots)q^{5}+\cdots\)
1849.4.a.e \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{7}+\beta _{9})q^{4}+\cdots\)
1849.4.a.f \(10\) \(109.095\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-5\) \(-19\) \(-51\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1849.4.a.g \(30\) \(109.095\) None \(-6\) \(-2\) \(-27\) \(-48\) \(-\)
1849.4.a.h \(30\) \(109.095\) None \(6\) \(2\) \(27\) \(48\) \(+\)
1849.4.a.i \(50\) \(109.095\) None \(-10\) \(-2\) \(8\) \(-6\) \(-\)
1849.4.a.j \(50\) \(109.095\) None \(10\) \(2\) \(-8\) \(6\) \(-\)
1849.4.a.k \(60\) \(109.095\) None \(-15\) \(-37\) \(-51\) \(-54\) \(-\)
1849.4.a.l \(60\) \(109.095\) None \(15\) \(37\) \(51\) \(54\) \(+\)
1849.4.a.m \(110\) \(109.095\) None \(0\) \(0\) \(0\) \(0\) \(+\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1849))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1849)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)