Properties

Label 1148.2.a
Level 1148
Weight 2
Character orbit a
Rep. character \(\chi_{1148}(1,\cdot)\)
Character field \(\Q\)
Dimension 20
Newforms 5
Sturm bound 336
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1148.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1148))\).

Total New Old
Modular forms 174 20 154
Cusp forms 163 20 143
Eisenstein series 11 0 11

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

\(2\)\(7\)\(41\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(10\)
Minus space\(-\)\(10\)

Trace form

\(20q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut +\mathstrut 28q^{39} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 28q^{61} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 44q^{69} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut -\mathstrut 52q^{75} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 44q^{87} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 41
1148.2.a.a \(2\) \(9.167\) \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots\)
1148.2.a.b \(3\) \(9.167\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(0\) \(3\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
1148.2.a.c \(5\) \(9.167\) 5.5.470117.1 None \(0\) \(-2\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
1148.2.a.d \(5\) \(9.167\) 5.5.287349.1 None \(0\) \(2\) \(-3\) \(-5\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
1148.2.a.e \(5\) \(9.167\) 5.5.1935333.1 None \(0\) \(2\) \(3\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)