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Properties

Label 133.4.a
Level $133$
Weight $4$
Character orbit 133.a
Rep. character $\chi_{133}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $5$
Sturm bound $53$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 133.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(53\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(133))\).

Total New Old
Modular forms 42 28 14
Cusp forms 38 28 10
Eisenstein series 4 0 4

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

\(7\)\(19\)FrickeDim
\(+\)\(+\)$+$\(7\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(15\)
Minus space\(-\)\(13\)

Trace form

\( 28 q - 2 q^{2} + 8 q^{3} + 110 q^{4} - 32 q^{5} + 60 q^{6} + 14 q^{7} - 78 q^{8} + 256 q^{9} + O(q^{10}) \) \( 28 q - 2 q^{2} + 8 q^{3} + 110 q^{4} - 32 q^{5} + 60 q^{6} + 14 q^{7} - 78 q^{8} + 256 q^{9} + 152 q^{10} + 116 q^{11} + 20 q^{12} - 152 q^{13} - 70 q^{14} - 192 q^{15} + 470 q^{16} + 56 q^{17} - 462 q^{18} - 464 q^{20} - 112 q^{21} - 580 q^{22} - 224 q^{23} + 848 q^{24} + 544 q^{25} - 316 q^{26} - 112 q^{27} - 98 q^{28} - 304 q^{29} + 84 q^{30} + 544 q^{31} - 406 q^{32} - 160 q^{33} - 392 q^{34} + 280 q^{35} - 458 q^{36} + 736 q^{37} + 112 q^{39} - 48 q^{40} - 1216 q^{41} + 28 q^{42} + 1204 q^{43} + 1248 q^{44} - 8 q^{45} - 280 q^{46} - 968 q^{47} + 1408 q^{48} + 1372 q^{49} + 1162 q^{50} - 800 q^{51} - 1428 q^{52} - 928 q^{53} + 2056 q^{54} - 1800 q^{55} - 462 q^{56} + 228 q^{57} - 976 q^{58} - 1880 q^{59} - 84 q^{60} - 1784 q^{61} + 2324 q^{62} + 630 q^{63} + 3058 q^{64} - 704 q^{65} + 640 q^{66} - 324 q^{67} + 2828 q^{68} + 600 q^{69} - 692 q^{71} - 4386 q^{72} + 120 q^{73} - 500 q^{74} - 1064 q^{75} - 336 q^{77} - 124 q^{78} - 588 q^{79} - 6924 q^{80} + 4188 q^{81} - 2680 q^{82} + 1168 q^{83} - 1792 q^{84} - 560 q^{85} - 1400 q^{86} - 2896 q^{87} - 924 q^{88} + 672 q^{89} + 6516 q^{90} - 336 q^{91} + 1076 q^{92} + 1784 q^{93} + 1092 q^{94} + 1520 q^{95} + 4612 q^{96} - 1848 q^{97} - 98 q^{98} + 3108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(133))\) 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 19
133.4.a.a 133.a 1.a $1$ $7.847$ \(\Q\) None \(4\) \(8\) \(6\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{3}+8q^{4}+6q^{5}+2^{5}q^{6}+\cdots\)
133.4.a.b 133.a 1.a $6$ $7.847$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-3\) \(-3\) \(-13\) \(-42\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
133.4.a.c 133.a 1.a $6$ $7.847$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(3\) \(7\) \(-29\) \(-42\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(4+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
133.4.a.d 133.a 1.a $7$ $7.847$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-8\) \(-17\) \(-33\) \(49\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
133.4.a.e 133.a 1.a $8$ $7.847$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(13\) \(37\) \(56\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(133))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(133)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)