Properties

Label 1078.2.a
Level $1078$
Weight $2$
Character orbit 1078.a
Rep. character $\chi_{1078}(1,\cdot)$
Character field $\Q$
Dimension $35$
Newform subspaces $24$
Sturm bound $336$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(336\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1078))\).

Total New Old
Modular forms 184 35 149
Cusp forms 153 35 118
Eisenstein series 31 0 31

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

\(2\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(21\)

Trace form

\( 35 q - q^{2} + 35 q^{4} - 2 q^{5} + 4 q^{6} - q^{8} + 39 q^{9} + O(q^{10}) \) \( 35 q - q^{2} + 35 q^{4} - 2 q^{5} + 4 q^{6} - q^{8} + 39 q^{9} - 6 q^{10} - q^{11} + 2 q^{13} + 16 q^{15} + 35 q^{16} + 6 q^{17} + 3 q^{18} + 12 q^{19} - 2 q^{20} - q^{22} + 8 q^{23} + 4 q^{24} + 37 q^{25} - 2 q^{26} + 24 q^{27} + 10 q^{29} + 24 q^{30} + 16 q^{31} - q^{32} - 2 q^{34} + 39 q^{36} - 54 q^{37} + 8 q^{38} - 32 q^{39} - 6 q^{40} - 18 q^{41} - 20 q^{43} - q^{44} - 34 q^{45} + 16 q^{46} - 16 q^{47} - 23 q^{50} + 2 q^{52} - 22 q^{53} + 16 q^{54} - 6 q^{55} - 40 q^{57} - 30 q^{58} - 8 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{62} + 35 q^{64} - 20 q^{65} + 4 q^{66} - 28 q^{67} + 6 q^{68} + 16 q^{71} + 3 q^{72} - 2 q^{73} - 22 q^{74} + 24 q^{75} + 12 q^{76} + 24 q^{78} - 56 q^{79} - 2 q^{80} + 43 q^{81} - 10 q^{82} + 4 q^{83} - 36 q^{85} + 12 q^{86} - 24 q^{87} - q^{88} - 18 q^{89} - 6 q^{90} + 8 q^{92} - 8 q^{93} + 8 q^{94} + 4 q^{96} - 18 q^{97} - 13 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 11
1078.2.a.a $1$ $8.608$ \(\Q\) None \(-1\) \(-3\) \(-4\) \(0\) $+$ $+$ $+$ \(q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{8}+\cdots\)
1078.2.a.b $1$ $8.608$ \(\Q\) None \(-1\) \(-2\) \(-2\) \(0\) $+$ $-$ $-$ \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
1078.2.a.c $1$ $8.608$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $-$ $+$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.d $1$ $8.608$ \(\Q\) None \(-1\) \(0\) \(4\) \(0\) $+$ $-$ $+$ \(q-q^{2}+q^{4}+4q^{5}-q^{8}-3q^{9}-4q^{10}+\cdots\)
1078.2.a.e $1$ $8.608$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $+$ $+$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.f $1$ $8.608$ \(\Q\) None \(-1\) \(3\) \(4\) \(0\) $+$ $-$ $+$ \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}-q^{8}+\cdots\)
1078.2.a.g $1$ $8.608$ \(\Q\) None \(1\) \(-3\) \(-2\) \(0\) $-$ $-$ $+$ \(q+q^{2}-3q^{3}+q^{4}-2q^{5}-3q^{6}+q^{8}+\cdots\)
1078.2.a.h $1$ $8.608$ \(\Q\) None \(1\) \(-2\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots\)
1078.2.a.i $1$ $8.608$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $-$ $+$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.j $1$ $8.608$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1078.2.a.k $1$ $8.608$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $+$ $+$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.l $1$ $8.608$ \(\Q\) None \(1\) \(2\) \(2\) \(0\) $-$ $-$ $-$ \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{8}+\cdots\)
1078.2.a.m $1$ $8.608$ \(\Q\) None \(1\) \(3\) \(2\) \(0\) $-$ $+$ $+$ \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{8}+\cdots\)
1078.2.a.n $2$ $8.608$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.o $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-3q^{9}-\beta q^{10}+\cdots\)
1078.2.a.p $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ \(q-q^{2}+q^{4}-2\beta q^{5}-q^{8}-3q^{9}+2\beta q^{10}+\cdots\)
1078.2.a.q $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
1078.2.a.r $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+5q^{9}+\cdots\)
1078.2.a.s $2$ $8.608$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $+$ $-$ \(q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.t $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) $-$ $+$ $-$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
1078.2.a.u $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ \(q+q^{2}+\beta q^{3}+q^{4}+3\beta q^{5}+\beta q^{6}+\cdots\)
1078.2.a.v $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ \(q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+q^{8}+\cdots\)
1078.2.a.w $2$ $8.608$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $-$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1078.2.a.x $2$ $8.608$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) $-$ $-$ $-$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1078))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1078)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 2}\)