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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 43
1849.4.a.a 1849.a 1.a $1$ $109.095$ \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-8q^{4}-3^{3}q^{9}+2^{5}q^{11}-90q^{13}+\cdots\)
1849.4.a.b 1849.a 1.a $4$ $109.095$ 4.4.45868.1 None \(4\) \(11\) \(27\) \(20\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
1849.4.a.c 1849.a 1.a $6$ $109.095$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(-7\) \(-43\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
1849.4.a.d 1849.a 1.a $10$ $109.095$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(5\) \(19\) \(51\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(2-\beta _{7}+\cdots)q^{5}+\cdots\)
1849.4.a.e 1849.a 1.a $10$ $109.095$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{7}+\beta _{9})q^{4}+\cdots\)
1849.4.a.f 1849.a 1.a $10$ $109.095$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-5\) \(-19\) \(-51\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1849.4.a.g 1849.a 1.a $30$ $109.095$ None \(-6\) \(-2\) \(-27\) \(-48\) $-$ $\mathrm{SU}(2)$
1849.4.a.h 1849.a 1.a $30$ $109.095$ None \(6\) \(2\) \(27\) \(48\) $+$ $\mathrm{SU}(2)$
1849.4.a.i 1849.a 1.a $50$ $109.095$ None \(-10\) \(-2\) \(8\) \(-6\) $-$ $\mathrm{SU}(2)$
1849.4.a.j 1849.a 1.a $50$ $109.095$ None \(10\) \(2\) \(-8\) \(6\) $-$ $\mathrm{SU}(2)$
1849.4.a.k 1849.a 1.a $60$ $109.095$ None \(-15\) \(-37\) \(-51\) \(-54\) $-$ $\mathrm{SU}(2)$
1849.4.a.l 1849.a 1.a $60$ $109.095$ None \(15\) \(37\) \(51\) \(54\) $+$ $\mathrm{SU}(2)$
1849.4.a.m 1849.a 1.a $110$ $109.095$ None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$

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

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