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Properties

Label 34.10.a
Level $34$
Weight $10$
Character orbit 34.a
Rep. character $\chi_{34}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $45$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 34 = 2 \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 34.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(45\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(34))\).

Total New Old
Modular forms 42 12 30
Cusp forms 38 12 26
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
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(4\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(7\)

Trace form

\( 12 q + 458 q^{3} + 3072 q^{4} - 4434 q^{5} + 1952 q^{6} + 9528 q^{7} + 85192 q^{9} + O(q^{10}) \) \( 12 q + 458 q^{3} + 3072 q^{4} - 4434 q^{5} + 1952 q^{6} + 9528 q^{7} + 85192 q^{9} - 71264 q^{10} + 27642 q^{11} + 117248 q^{12} - 306444 q^{13} - 90816 q^{14} + 844256 q^{15} + 786432 q^{16} - 167042 q^{17} + 509760 q^{18} - 869344 q^{19} - 1135104 q^{20} + 2624424 q^{21} + 1277344 q^{22} - 3663012 q^{23} + 499712 q^{24} + 3484072 q^{25} + 684864 q^{26} + 6109076 q^{27} + 2439168 q^{28} + 3400230 q^{29} + 1142400 q^{30} - 2230480 q^{31} - 4658548 q^{33} - 2672672 q^{34} + 5588136 q^{35} + 21809152 q^{36} - 1578878 q^{37} + 819840 q^{38} + 25906748 q^{39} - 18243584 q^{40} + 13455468 q^{41} + 3849856 q^{42} - 18248884 q^{43} + 7076352 q^{44} - 161201178 q^{45} + 16444032 q^{46} - 62840400 q^{47} + 30015488 q^{48} + 180692140 q^{49} + 191538624 q^{50} - 13530402 q^{51} - 78449664 q^{52} - 192828684 q^{53} - 143109184 q^{54} - 44799152 q^{55} - 23248896 q^{56} - 597691784 q^{57} + 102851616 q^{58} - 72994188 q^{59} + 216129536 q^{60} - 30242550 q^{61} - 238261824 q^{62} + 352116128 q^{63} + 201326592 q^{64} + 125818836 q^{65} - 1086400 q^{66} + 51936220 q^{67} - 42762752 q^{68} + 254784096 q^{69} - 141304576 q^{70} + 162035340 q^{71} + 130498560 q^{72} + 191658016 q^{73} + 217784160 q^{74} - 908817970 q^{75} - 222552064 q^{76} - 334926312 q^{77} + 1284908608 q^{78} - 214523620 q^{79} - 290586624 q^{80} + 2789532352 q^{81} - 340908608 q^{82} + 1155316572 q^{83} + 671852544 q^{84} + 124112206 q^{85} - 625871424 q^{86} - 667080912 q^{87} + 327000064 q^{88} + 696477960 q^{89} - 1897968352 q^{90} - 449407720 q^{91} - 937731072 q^{92} - 1865251656 q^{93} + 173675776 q^{94} + 138672840 q^{95} + 127926272 q^{96} - 351391908 q^{97} - 578568960 q^{98} + 3788248322 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(34))\) 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
34.10.a.a 34.a 1.a $2$ $17.511$ \(\Q(\sqrt{43}) \) None \(32\) \(64\) \(-2788\) \(-728\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(2^{5}+\beta )q^{3}+2^{8}q^{4}+(-1394+\cdots)q^{5}+\cdots\)
34.10.a.b 34.a 1.a $3$ $17.511$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-48\) \(84\) \(-1304\) \(690\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(28-\beta _{1})q^{3}+2^{8}q^{4}+(-435+\cdots)q^{5}+\cdots\)
34.10.a.c 34.a 1.a $3$ $17.511$ 3.3.3262740.1 None \(-48\) \(84\) \(1314\) \(6912\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(28-\beta _{2})q^{3}+2^{8}q^{4}+(438+\cdots)q^{5}+\cdots\)
34.10.a.d 34.a 1.a $4$ $17.511$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(64\) \(226\) \(-1656\) \(2654\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(57+\beta _{1})q^{3}+2^{8}q^{4}+(-412+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(34))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(34)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)