Properties

Label 35.4.a
Level $35$
Weight $4$
Character orbit 35.a
Rep. character $\chi_{35}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(35))\).

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
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.

\(5\)\(7\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(1\)

Trace form

\( 6 q + 6 q^{2} - 4 q^{3} + 26 q^{4} + 8 q^{6} + 14 q^{7} + 18 q^{8} + 130 q^{9} + O(q^{10}) \) \( 6 q + 6 q^{2} - 4 q^{3} + 26 q^{4} + 8 q^{6} + 14 q^{7} + 18 q^{8} + 130 q^{9} - 60 q^{10} - 76 q^{11} - 204 q^{12} + 16 q^{13} - 70 q^{14} + 40 q^{15} + 130 q^{16} - 196 q^{17} - 358 q^{18} + 244 q^{19} - 56 q^{21} + 12 q^{22} + 152 q^{23} + 44 q^{24} + 150 q^{25} - 308 q^{26} + 176 q^{27} - 98 q^{28} + 256 q^{29} + 200 q^{30} - 48 q^{31} + 650 q^{32} + 296 q^{33} + 464 q^{34} + 140 q^{35} - 214 q^{36} + 76 q^{37} - 100 q^{38} - 372 q^{39} - 240 q^{40} + 436 q^{41} + 168 q^{42} - 344 q^{43} - 1512 q^{44} + 160 q^{45} + 400 q^{46} - 544 q^{47} - 1900 q^{48} + 294 q^{49} + 150 q^{50} - 1180 q^{51} + 2376 q^{52} + 76 q^{53} + 388 q^{54} - 360 q^{55} - 546 q^{56} - 1944 q^{57} + 392 q^{58} - 1972 q^{59} - 500 q^{60} + 1280 q^{61} - 984 q^{62} + 742 q^{63} + 1570 q^{64} + 360 q^{65} + 1348 q^{66} - 112 q^{67} + 2484 q^{68} + 360 q^{69} + 140 q^{70} - 1368 q^{71} - 590 q^{72} + 1068 q^{73} + 2084 q^{74} - 100 q^{75} + 3284 q^{76} - 336 q^{77} + 3972 q^{78} - 1020 q^{79} - 1440 q^{80} + 470 q^{81} - 420 q^{82} - 2484 q^{83} + 84 q^{84} + 460 q^{85} - 72 q^{86} - 1584 q^{87} - 4888 q^{88} - 844 q^{89} - 2320 q^{90} - 588 q^{91} + 136 q^{92} + 6120 q^{93} - 2500 q^{94} + 460 q^{95} - 6908 q^{96} + 3868 q^{97} + 294 q^{98} - 2104 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(35))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7
35.4.a.a 35.a 1.a $1$ $2.065$ \(\Q\) None \(1\) \(-8\) \(-5\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots\)
35.4.a.b 35.a 1.a $2$ $2.065$ \(\Q(\sqrt{2}) \) None \(8\) \(2\) \(-10\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(4+\beta )q^{2}+(1-4\beta )q^{3}+(10+8\beta )q^{4}+\cdots\)
35.4.a.c 35.a 1.a $3$ $2.065$ 3.3.14360.1 None \(-3\) \(2\) \(15\) \(21\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(35))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(35)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)