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Properties

Label 833.4.a
Level $833$
Weight $4$
Character orbit 833.a
Rep. character $\chi_{833}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $15$
Sturm bound $336$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 833.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(336\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(833))\).

Total New Old
Modular forms 260 164 96
Cusp forms 244 164 80
Eisenstein series 16 0 16

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

\(7\)\(17\)FrickeDim
\(+\)\(+\)$+$\(42\)
\(+\)\(-\)$-$\(38\)
\(-\)\(+\)$-$\(39\)
\(-\)\(-\)$+$\(45\)
Plus space\(+\)\(87\)
Minus space\(-\)\(77\)

Trace form

\( 164 q + 2 q^{2} - 4 q^{3} + 646 q^{4} + 18 q^{5} - 10 q^{6} + 30 q^{8} + 1480 q^{9} + O(q^{10}) \) \( 164 q + 2 q^{2} - 4 q^{3} + 646 q^{4} + 18 q^{5} - 10 q^{6} + 30 q^{8} + 1480 q^{9} - 70 q^{10} - 36 q^{11} - 34 q^{12} - 20 q^{13} + 68 q^{15} + 2766 q^{16} + 34 q^{17} + 110 q^{18} - 172 q^{19} - 270 q^{20} - 274 q^{22} - 278 q^{23} - 354 q^{24} + 4320 q^{25} - 184 q^{26} - 100 q^{27} - 162 q^{29} + 20 q^{30} - 90 q^{31} + 462 q^{32} + 180 q^{33} + 68 q^{34} + 7158 q^{36} - 1310 q^{37} + 716 q^{38} - 1476 q^{39} + 1262 q^{40} + 276 q^{41} - 1600 q^{43} + 1450 q^{44} - 94 q^{45} + 76 q^{46} + 680 q^{47} + 1738 q^{48} + 62 q^{50} - 204 q^{51} + 100 q^{52} - 1852 q^{53} + 2488 q^{54} + 124 q^{55} + 2632 q^{57} - 202 q^{58} + 504 q^{59} + 3724 q^{60} - 1082 q^{61} + 3040 q^{62} + 11850 q^{64} + 284 q^{65} + 1484 q^{66} + 1388 q^{67} + 408 q^{68} - 1528 q^{69} - 630 q^{71} - 358 q^{72} - 1064 q^{73} - 1894 q^{74} - 348 q^{75} - 988 q^{76} - 416 q^{78} + 594 q^{79} + 402 q^{80} + 14376 q^{81} + 1276 q^{82} - 872 q^{83} + 238 q^{85} - 5920 q^{86} - 588 q^{87} - 14778 q^{88} - 3184 q^{89} + 2342 q^{90} - 6844 q^{92} + 5624 q^{93} + 204 q^{94} - 3128 q^{95} - 1066 q^{96} + 1140 q^{97} - 2120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(833))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 17
833.4.a.a 833.a 1.a $1$ $49.149$ \(\Q\) None \(-3\) \(8\) \(-6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
833.4.a.b 833.a 1.a $1$ $49.149$ \(\Q\) None \(-1\) \(6\) \(20\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots\)
833.4.a.c 833.a 1.a $3$ $49.149$ 3.3.2429.1 None \(-1\) \(-5\) \(19\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
833.4.a.d 833.a 1.a $3$ $49.149$ 3.3.2636.1 None \(1\) \(-4\) \(8\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
833.4.a.e 833.a 1.a $4$ $49.149$ 4.4.68557.1 None \(-2\) \(7\) \(9\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
833.4.a.f 833.a 1.a $7$ $49.149$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(-5\) \(-35\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
833.4.a.g 833.a 1.a $9$ $49.149$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(2\) \(-11\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
833.4.a.h 833.a 1.a $12$ $49.149$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-12\) \(-34\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
833.4.a.i 833.a 1.a $12$ $49.149$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(12\) \(34\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{6})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
833.4.a.j 833.a 1.a $14$ $49.149$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-5\) \(-6\) \(-10\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
833.4.a.k 833.a 1.a $14$ $49.149$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-5\) \(6\) \(10\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
833.4.a.l 833.a 1.a $18$ $49.149$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(3\) \(-6\) \(-10\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
833.4.a.m 833.a 1.a $18$ $49.149$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(3\) \(6\) \(10\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
833.4.a.n 833.a 1.a $24$ $49.149$ None \(2\) \(-24\) \(-20\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
833.4.a.o 833.a 1.a $24$ $49.149$ None \(2\) \(24\) \(20\) \(0\) $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(833))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(833)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 2}\)