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

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

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

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