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Properties

Label 1911.4.a
Level $1911$
Weight $4$
Character orbit 1911.a
Rep. character $\chi_{1911}(1,\cdot)$
Character field $\Q$
Dimension $246$
Newform subspaces $33$
Sturm bound $1045$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 33 \)
Sturm bound: \(1045\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1911))\).

Total New Old
Modular forms 800 246 554
Cusp forms 768 246 522
Eisenstein series 32 0 32

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

\(3\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(33\)
\(+\)\(+\)\(-\)$-$\(27\)
\(+\)\(-\)\(+\)$-$\(30\)
\(+\)\(-\)\(-\)$+$\(33\)
\(-\)\(+\)\(+\)$-$\(25\)
\(-\)\(+\)\(-\)$+$\(35\)
\(-\)\(-\)\(+\)$+$\(36\)
\(-\)\(-\)\(-\)$-$\(27\)
Plus space\(+\)\(137\)
Minus space\(-\)\(109\)

Trace form

\( 246 q - 4 q^{2} + 1016 q^{4} - 16 q^{5} - 24 q^{6} - 48 q^{8} + 2214 q^{9} + O(q^{10}) \) \( 246 q - 4 q^{2} + 1016 q^{4} - 16 q^{5} - 24 q^{6} - 48 q^{8} + 2214 q^{9} - 12 q^{10} + 96 q^{11} + 12 q^{12} - 26 q^{13} + 144 q^{15} + 3964 q^{16} + 188 q^{17} - 36 q^{18} - 88 q^{19} + 92 q^{20} + 220 q^{22} + 120 q^{23} - 468 q^{24} + 5986 q^{25} - 580 q^{29} - 492 q^{30} - 416 q^{31} - 28 q^{32} - 872 q^{34} + 9144 q^{36} + 52 q^{37} + 2200 q^{38} + 156 q^{39} + 748 q^{40} + 424 q^{41} + 1008 q^{43} + 1044 q^{44} - 144 q^{45} - 360 q^{46} + 1008 q^{47} + 624 q^{48} + 1524 q^{50} - 1032 q^{51} - 780 q^{52} + 140 q^{53} - 216 q^{54} + 2304 q^{55} + 1308 q^{57} + 936 q^{58} + 1072 q^{59} + 828 q^{60} + 1548 q^{61} + 264 q^{62} + 17296 q^{64} + 416 q^{65} - 1764 q^{66} + 2744 q^{67} - 1424 q^{68} + 1416 q^{69} + 1408 q^{71} - 432 q^{72} + 364 q^{73} - 1648 q^{74} - 72 q^{75} - 3032 q^{76} + 156 q^{78} - 1376 q^{79} + 2036 q^{80} + 19926 q^{81} - 932 q^{82} + 4688 q^{83} + 272 q^{85} + 17384 q^{86} + 624 q^{87} + 12156 q^{88} + 896 q^{89} - 108 q^{90} + 11528 q^{92} - 1308 q^{93} - 372 q^{94} + 4584 q^{95} - 1848 q^{96} - 1780 q^{97} + 864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 13
1911.4.a.a 1911.a 1.a $1$ $112.753$ \(\Q\) None \(-5\) \(-3\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}-3q^{3}+17q^{4}+3q^{5}+15q^{6}+\cdots\)
1911.4.a.b 1911.a 1.a $1$ $112.753$ \(\Q\) None \(-5\) \(3\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{2}+3q^{3}+17q^{4}-3q^{5}-15q^{6}+\cdots\)
1911.4.a.c 1911.a 1.a $1$ $112.753$ \(\Q\) None \(-4\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+3q^{3}+8q^{4}-12q^{6}+9q^{9}+\cdots\)
1911.4.a.d 1911.a 1.a $1$ $112.753$ \(\Q\) None \(-1\) \(-3\) \(-9\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}-9q^{5}+3q^{6}+\cdots\)
1911.4.a.e 1911.a 1.a $1$ $112.753$ \(\Q\) None \(-1\) \(-3\) \(5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
1911.4.a.f 1911.a 1.a $1$ $112.753$ \(\Q\) None \(0\) \(3\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-8q^{4}+12q^{5}+9q^{9}-6^{2}q^{11}+\cdots\)
1911.4.a.g 1911.a 1.a $2$ $112.753$ \(\Q(\sqrt{865}) \) None \(2\) \(6\) \(-5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}+(-3+\beta )q^{5}+\cdots\)
1911.4.a.h 1911.a 1.a $2$ $112.753$ \(\Q(\sqrt{14}) \) None \(2\) \(6\) \(-24\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3q^{3}+(7+2\beta )q^{4}+(-12+\cdots)q^{5}+\cdots\)
1911.4.a.i 1911.a 1.a $3$ $112.753$ 3.3.4001.1 None \(0\) \(-9\) \(27\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.j 1911.a 1.a $3$ $112.753$ 3.3.4001.1 None \(0\) \(9\) \(-27\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.k 1911.a 1.a $3$ $112.753$ 3.3.3144.1 None \(2\) \(-9\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.l 1911.a 1.a $4$ $112.753$ 4.4.1038472.1 None \(-3\) \(-12\) \(24\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.m 1911.a 1.a $4$ $112.753$ 4.4.6295500.1 None \(-3\) \(12\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(3-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.n 1911.a 1.a $5$ $112.753$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(5\) \(15\) \(-15\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1911.4.a.o 1911.a 1.a $6$ $112.753$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(18\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.p 1911.a 1.a $6$ $112.753$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-18\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.4.a.q 1911.a 1.a $6$ $112.753$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(7\) \(-18\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(4+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.r 1911.a 1.a $7$ $112.753$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-21\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.4.a.s 1911.a 1.a $7$ $112.753$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(21\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1911.4.a.t 1911.a 1.a $7$ $112.753$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(8\) \(-21\) \(-21\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.u 1911.a 1.a $7$ $112.753$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(8\) \(21\) \(21\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1911.4.a.v 1911.a 1.a $11$ $112.753$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-1\) \(-33\) \(17\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.4.a.w 1911.a 1.a $11$ $112.753$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-1\) \(33\) \(-17\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.x 1911.a 1.a $11$ $112.753$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(1\) \(-33\) \(18\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}+(2+\beta _{5}+\cdots)q^{5}+\cdots\)
1911.4.a.y 1911.a 1.a $11$ $112.753$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(1\) \(33\) \(-18\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1911.4.a.z 1911.a 1.a $13$ $112.753$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(-39\) \(-39\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-3+\cdots)q^{5}+\cdots\)
1911.4.a.ba 1911.a 1.a $13$ $112.753$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(39\) \(39\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(3+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.4.a.bb 1911.a 1.a $13$ $112.753$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(-39\) \(-15\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1911.4.a.bc 1911.a 1.a $13$ $112.753$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(39\) \(15\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{8}+\cdots)q^{5}+\cdots\)
1911.4.a.bd 1911.a 1.a $14$ $112.753$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-6\) \(-42\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
1911.4.a.be 1911.a 1.a $14$ $112.753$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-6\) \(42\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
1911.4.a.bf 1911.a 1.a $22$ $112.753$ None \(2\) \(-66\) \(-36\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$
1911.4.a.bg 1911.a 1.a $22$ $112.753$ None \(2\) \(66\) \(36\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1911))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1911)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)