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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

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7
105.4.a.a \(1\) \(6.195\) \(\Q\) None \(0\) \(-3\) \(5\) \(7\) \(+\) \(-\) \(-\) \(q-3q^{3}-8q^{4}+5q^{5}+7q^{7}+9q^{9}+\cdots\)
105.4.a.b \(1\) \(6.195\) \(\Q\) None \(5\) \(-3\) \(5\) \(7\) \(+\) \(-\) \(-\) \(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
105.4.a.c \(2\) \(6.195\) \(\Q(\sqrt{17}) \) None \(-7\) \(-6\) \(-10\) \(-14\) \(+\) \(+\) \(+\) \(q+(-3-\beta )q^{2}-3q^{3}+(5+7\beta )q^{4}+\cdots\)
105.4.a.d \(2\) \(6.195\) \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(-10\) \(-14\) \(-\) \(+\) \(+\) \(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
105.4.a.e \(2\) \(6.195\) \(\Q(\sqrt{2}) \) None \(-2\) \(-6\) \(10\) \(-14\) \(+\) \(-\) \(+\) \(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
105.4.a.f \(2\) \(6.195\) \(\Q(\sqrt{65}) \) None \(1\) \(6\) \(10\) \(-14\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+3q^{3}+(8+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
105.4.a.g \(2\) \(6.195\) \(\Q(\sqrt{41}) \) None \(3\) \(6\) \(-10\) \(14\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}-5q^{5}+\cdots\)

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

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