Properties

Label 105.4.a
Level $105$
Weight $4$
Character orbit 105.a
Rep. character $\chi_{105}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $7$
Sturm bound $64$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(64\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(105))\).

Total New Old
Modular forms 52 12 40
Cusp forms 44 12 32
Eisenstein series 8 0 8

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
Plus space\(+\)\(8\)
Minus space\(-\)\(4\)

Trace form

\( 12 q - 4 q^{2} + 56 q^{4} + 12 q^{6} - 28 q^{7} + 36 q^{8} + 108 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{2} + 56 q^{4} + 12 q^{6} - 28 q^{7} + 36 q^{8} + 108 q^{9} + 60 q^{10} - 40 q^{11} - 32 q^{13} + 140 q^{14} - 60 q^{15} + 328 q^{16} - 64 q^{17} - 36 q^{18} - 104 q^{19} + 72 q^{22} + 248 q^{23} + 324 q^{24} + 300 q^{25} - 160 q^{26} - 140 q^{28} - 240 q^{29} - 120 q^{30} + 288 q^{31} - 596 q^{32} - 192 q^{33} - 928 q^{34} + 504 q^{36} - 56 q^{37} - 648 q^{38} - 24 q^{39} + 420 q^{40} - 80 q^{41} - 168 q^{42} - 416 q^{43} - 432 q^{44} - 1040 q^{46} + 272 q^{47} - 1248 q^{48} + 588 q^{49} - 100 q^{50} + 864 q^{51} - 216 q^{52} + 1824 q^{53} + 108 q^{54} + 360 q^{55} + 1092 q^{56} - 456 q^{57} + 920 q^{58} - 304 q^{59} + 180 q^{60} - 1408 q^{61} - 696 q^{62} - 252 q^{63} - 488 q^{64} - 320 q^{65} + 624 q^{66} - 976 q^{67} - 3088 q^{68} - 1008 q^{69} - 280 q^{70} + 1408 q^{71} + 324 q^{72} + 2592 q^{73} + 688 q^{74} - 3952 q^{76} + 1904 q^{77} - 2856 q^{78} + 2544 q^{79} - 1760 q^{80} + 972 q^{81} - 3096 q^{82} + 2000 q^{83} - 440 q^{85} + 1800 q^{86} + 240 q^{87} + 6872 q^{88} - 3392 q^{89} + 540 q^{90} + 840 q^{91} + 4760 q^{92} + 72 q^{93} - 472 q^{94} + 40 q^{95} + 1644 q^{96} - 3776 q^{97} - 196 q^{98} - 360 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(105))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7
105.4.a.a 105.a 1.a $1$ $6.195$ \(\Q\) None \(0\) \(-3\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-8q^{4}+5q^{5}+7q^{7}+9q^{9}+\cdots\)
105.4.a.b 105.a 1.a $1$ $6.195$ \(\Q\) None \(5\) \(-3\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
105.4.a.c 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{17}) \) None \(-7\) \(-6\) \(-10\) \(-14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{2}-3q^{3}+(5+7\beta )q^{4}+\cdots\)
105.4.a.d 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(-10\) \(-14\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
105.4.a.e 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{2}) \) None \(-2\) \(-6\) \(10\) \(-14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
105.4.a.f 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{65}) \) None \(1\) \(6\) \(10\) \(-14\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(8+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
105.4.a.g 105.a 1.a $2$ $6.195$ \(\Q(\sqrt{41}) \) None \(3\) \(6\) \(-10\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}-5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(105))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(105)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)