Properties

Label 2678.2.a
Level 2678
Weight 2
Character orbit a
Rep. character \(\chi_{2678}(1,\cdot)\)
Character field \(\Q\)
Dimension 101
Newforms 23
Sturm bound 728
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2678.a (trivial)
Character field: \(\Q\)
Newforms: \( 23 \)
Sturm bound: \(728\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2678))\).

Total New Old
Modular forms 368 101 267
Cusp forms 361 101 260
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.

\(2\)\(13\)\(103\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(14\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(41\)
Minus space\(-\)\(60\)

Trace form

\(101q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 101q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 93q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(101q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 101q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 93q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 101q^{16} \) \(\mathstrut +\mathstrut 22q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 87q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut +\mathstrut 36q^{27} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 28q^{35} \) \(\mathstrut +\mathstrut 93q^{36} \) \(\mathstrut -\mathstrut 22q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 28q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 121q^{49} \) \(\mathstrut +\mathstrut 47q^{50} \) \(\mathstrut +\mathstrut 44q^{51} \) \(\mathstrut +\mathstrut q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 101q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut +\mathstrut 22q^{68} \) \(\mathstrut -\mathstrut 48q^{69} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 3q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 30q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 93q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 16q^{86} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 86q^{89} \) \(\mathstrut -\mathstrut 34q^{90} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut -\mathstrut 32q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2678))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 13 103
2678.2.a.a \(1\) \(21.384\) \(\Q\) None \(-1\) \(-2\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{7}+\cdots\)
2678.2.a.b \(1\) \(21.384\) \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
2678.2.a.c \(1\) \(21.384\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(-3\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots\)
2678.2.a.d \(1\) \(21.384\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
2678.2.a.e \(1\) \(21.384\) \(\Q\) None \(-1\) \(2\) \(-2\) \(3\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+3q^{7}+\cdots\)
2678.2.a.f \(1\) \(21.384\) \(\Q\) None \(-1\) \(2\) \(0\) \(-5\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-5q^{7}-q^{8}+\cdots\)
2678.2.a.g \(1\) \(21.384\) \(\Q\) None \(-1\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
2678.2.a.h \(1\) \(21.384\) \(\Q\) None \(-1\) \(3\) \(1\) \(5\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}+5q^{7}+\cdots\)
2678.2.a.i \(1\) \(21.384\) \(\Q\) None \(1\) \(-2\) \(-4\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}-3q^{7}+\cdots\)
2678.2.a.j \(1\) \(21.384\) \(\Q\) None \(1\) \(-2\) \(2\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}-3q^{7}+\cdots\)
2678.2.a.k \(1\) \(21.384\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
2678.2.a.l \(1\) \(21.384\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
2678.2.a.m \(1\) \(21.384\) \(\Q\) None \(1\) \(1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
2678.2.a.n \(1\) \(21.384\) \(\Q\) None \(1\) \(3\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+4q^{7}+\cdots\)
2678.2.a.o \(2\) \(21.384\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}-2\beta q^{5}+\cdots\)
2678.2.a.p \(3\) \(21.384\) 3.3.621.1 None \(-3\) \(-3\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
2678.2.a.q \(3\) \(21.384\) 3.3.316.1 None \(3\) \(-4\) \(0\) \(-5\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
2678.2.a.r \(10\) \(21.384\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(0\) \(9\) \(9\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{3})q^{5}-\beta _{1}q^{6}+\cdots\)
2678.2.a.s \(10\) \(21.384\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-6\) \(-3\) \(-10\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+\cdots\)
2678.2.a.t \(11\) \(21.384\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(6\) \(7\) \(7\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{5})q^{5}+\cdots\)
2678.2.a.u \(14\) \(21.384\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(-5\) \(-11\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
2678.2.a.v \(15\) \(21.384\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(0\) \(3\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
2678.2.a.w \(19\) \(21.384\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(19\) \(6\) \(1\) \(13\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2678))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2678)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1339))\)\(^{\oplus 2}\)