Properties

Label 1144.2.a
Level 1144
Weight 2
Character orbit a
Rep. character \(\chi_{1144}(1,\cdot)\)
Character field \(\Q\)
Dimension 30
Newforms 12
Sturm bound 336
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1144 = 2^{3} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1144.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(336\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1144))\).

Total New Old
Modular forms 176 30 146
Cusp forms 161 30 131
Eisenstein series 15 0 15

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

\(2\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(18\)

Trace form

\(30q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 30q^{25} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 28q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 72q^{63} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut 72q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 30q^{81} \) \(\mathstrut -\mathstrut 48q^{87} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 44q^{93} \) \(\mathstrut +\mathstrut 40q^{95} \) \(\mathstrut -\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 13
1144.2.a.a \(1\) \(9.135\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
1144.2.a.b \(1\) \(9.135\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
1144.2.a.c \(1\) \(9.135\) \(\Q\) None \(0\) \(2\) \(3\) \(1\) \(-\) \(+\) \(+\) \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
1144.2.a.d \(1\) \(9.135\) \(\Q\) None \(0\) \(3\) \(3\) \(-3\) \(+\) \(-\) \(+\) \(q+3q^{3}+3q^{5}-3q^{7}+6q^{9}+q^{11}+\cdots\)
1144.2.a.e \(2\) \(9.135\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(-5\) \(-\) \(+\) \(+\) \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
1144.2.a.f \(2\) \(9.135\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(1\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{3}-2\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1144.2.a.g \(2\) \(9.135\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+(2-3\beta )q^{7}+\cdots\)
1144.2.a.h \(3\) \(9.135\) 3.3.229.1 None \(0\) \(0\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
1144.2.a.i \(3\) \(9.135\) 3.3.229.1 None \(0\) \(0\) \(1\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
1144.2.a.j \(3\) \(9.135\) 3.3.229.1 None \(0\) \(3\) \(1\) \(6\) \(+\) \(+\) \(-\) \(q+(1+\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
1144.2.a.k \(5\) \(9.135\) 5.5.7698829.1 None \(0\) \(0\) \(-4\) \(6\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1144.2.a.l \(6\) \(9.135\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-1\) \(5\) \(-1\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+\beta _{5}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1144))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1144)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)