Properties

Label 6378.2.a
Level $6378$
Weight $2$
Character orbit 6378.a
Rep. character $\chi_{6378}(1,\cdot)$
Character field $\Q$
Dimension $177$
Newform subspaces $15$
Sturm bound $2128$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6378 = 2 \cdot 3 \cdot 1063 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6378.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(2128\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6378))\).

Total New Old
Modular forms 1068 177 891
Cusp forms 1061 177 884
Eisenstein series 7 0 7

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

\(2\)\(3\)\(1063\)FrickeDim
\(+\)\(+\)\(+\)$+$\(23\)
\(+\)\(+\)\(-\)$-$\(21\)
\(+\)\(-\)\(+\)$-$\(21\)
\(+\)\(-\)\(-\)$+$\(23\)
\(-\)\(+\)\(+\)$-$\(28\)
\(-\)\(+\)\(-\)$+$\(17\)
\(-\)\(-\)\(+\)$+$\(17\)
\(-\)\(-\)\(-\)$-$\(27\)
Plus space\(+\)\(80\)
Minus space\(-\)\(97\)

Trace form

\( 177 q + q^{2} - q^{3} + 177 q^{4} + 6 q^{5} - q^{6} + q^{8} + 177 q^{9} + O(q^{10}) \) \( 177 q + q^{2} - q^{3} + 177 q^{4} + 6 q^{5} - q^{6} + q^{8} + 177 q^{9} - 2 q^{10} - 4 q^{11} - q^{12} - 6 q^{13} - 6 q^{15} + 177 q^{16} + 10 q^{17} + q^{18} - 8 q^{19} + 6 q^{20} - 8 q^{21} + 16 q^{23} - q^{24} + 179 q^{25} + 6 q^{26} - q^{27} + 14 q^{29} - 2 q^{30} - 8 q^{31} + q^{32} - 4 q^{33} + 10 q^{34} + 24 q^{35} + 177 q^{36} + 10 q^{37} + 20 q^{38} - 6 q^{39} - 2 q^{40} + 2 q^{41} - 8 q^{42} + 4 q^{43} - 4 q^{44} + 6 q^{45} + 32 q^{47} - q^{48} + 177 q^{49} + 31 q^{50} + 6 q^{51} - 6 q^{52} + 38 q^{53} - q^{54} + 32 q^{55} - 20 q^{57} - 2 q^{58} + 4 q^{59} - 6 q^{60} - 10 q^{61} + 177 q^{64} + 36 q^{65} - 4 q^{66} - 16 q^{67} + 10 q^{68} - 8 q^{69} - 32 q^{70} - 8 q^{71} + q^{72} - 6 q^{73} + 6 q^{74} - 31 q^{75} - 8 q^{76} + 48 q^{77} - 14 q^{78} - 16 q^{79} + 6 q^{80} + 177 q^{81} - 6 q^{82} - 4 q^{83} - 8 q^{84} - 12 q^{85} - 28 q^{86} + 2 q^{87} - 6 q^{89} - 2 q^{90} - 40 q^{91} + 16 q^{92} - 28 q^{93} - 8 q^{94} + 24 q^{95} - q^{96} - 22 q^{97} + 41 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6378))\) 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 3 1063
6378.2.a.a 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
6378.2.a.b 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
6378.2.a.c 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
6378.2.a.d 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
6378.2.a.e 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(1\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
6378.2.a.f 6378.a 1.a $1$ $50.929$ \(\Q\) None \(1\) \(1\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
6378.2.a.g 6378.a 1.a $2$ $50.929$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
6378.2.a.h 6378.a 1.a $12$ $50.929$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(12\) \(-13\) \(-15\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
6378.2.a.i 6378.a 1.a $16$ $50.929$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(-16\) \(-10\) \(-12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
6378.2.a.j 6378.a 1.a $21$ $50.929$ None \(-21\) \(-21\) \(1\) \(15\) $+$ $+$ $-$ $\mathrm{SU}(2)$
6378.2.a.k 6378.a 1.a $21$ $50.929$ None \(-21\) \(21\) \(9\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$
6378.2.a.l 6378.a 1.a $23$ $50.929$ None \(-23\) \(-23\) \(2\) \(-15\) $+$ $+$ $+$ $\mathrm{SU}(2)$
6378.2.a.m 6378.a 1.a $23$ $50.929$ None \(-23\) \(23\) \(-8\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$
6378.2.a.n 6378.a 1.a $26$ $50.929$ None \(26\) \(26\) \(13\) \(16\) $-$ $-$ $-$ $\mathrm{SU}(2)$
6378.2.a.o 6378.a 1.a $27$ $50.929$ None \(27\) \(-27\) \(15\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6378))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6378)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1063))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3189))\)\(^{\oplus 2}\)