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Properties

Label 34.4.a
Level $34$
Weight $4$
Character orbit 34.a
Rep. character $\chi_{34}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $18$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 34 = 2 \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 34.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(34))\).

Total New Old
Modular forms 16 4 12
Cusp forms 12 4 8
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.

\(2\)\(17\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\( 4 q + 2 q^{3} + 16 q^{4} - 6 q^{5} + 20 q^{6} + 8 q^{7} - 56 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 16 q^{4} - 6 q^{5} + 20 q^{6} + 8 q^{7} - 56 q^{9} - 4 q^{10} + 50 q^{11} + 8 q^{12} - 52 q^{13} - 40 q^{14} - 112 q^{15} + 64 q^{16} + 34 q^{17} + 72 q^{18} - 144 q^{19} - 24 q^{20} - 72 q^{21} - 124 q^{22} - 84 q^{23} + 80 q^{24} + 504 q^{25} - 152 q^{26} + 164 q^{27} + 32 q^{28} + 418 q^{29} - 240 q^{30} - 432 q^{31} + 260 q^{33} + 68 q^{34} + 680 q^{35} - 224 q^{36} + 70 q^{37} + 144 q^{38} - 580 q^{39} - 16 q^{40} + 516 q^{41} - 32 q^{42} - 564 q^{43} + 200 q^{44} - 558 q^{45} + 336 q^{46} - 416 q^{47} + 32 q^{48} - 652 q^{49} - 312 q^{50} + 102 q^{51} - 208 q^{52} - 692 q^{53} - 472 q^{54} - 448 q^{55} - 160 q^{56} + 472 q^{57} + 876 q^{58} + 756 q^{59} - 448 q^{60} + 878 q^{61} + 1208 q^{62} - 448 q^{63} + 256 q^{64} - 740 q^{65} + 968 q^{66} - 644 q^{67} + 136 q^{68} + 144 q^{69} - 896 q^{70} + 1884 q^{71} + 288 q^{72} + 736 q^{73} + 1220 q^{74} + 278 q^{75} - 576 q^{76} + 1176 q^{77} - 1064 q^{78} - 2052 q^{79} - 96 q^{80} + 640 q^{81} + 584 q^{82} - 452 q^{83} - 288 q^{84} - 646 q^{85} - 1352 q^{86} + 1824 q^{87} - 496 q^{88} - 920 q^{89} - 1300 q^{90} - 1672 q^{91} - 336 q^{92} + 696 q^{93} + 608 q^{94} - 120 q^{95} + 320 q^{96} - 1804 q^{97} - 1264 q^{98} + 1082 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(34))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 17
34.4.a.a 34.a 1.a $1$ $2.006$ \(\Q\) None \(-2\) \(-2\) \(-18\) \(-10\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}-18q^{5}+4q^{6}+\cdots\)
34.4.a.b 34.a 1.a $1$ $2.006$ \(\Q\) None \(-2\) \(-2\) \(16\) \(24\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+2^{4}q^{5}+4q^{6}+\cdots\)
34.4.a.c 34.a 1.a $2$ $2.006$ \(\Q(\sqrt{13}) \) None \(4\) \(6\) \(-4\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(3+\beta )q^{3}+4q^{4}+(-2-4\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(34))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(34)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)