Properties

Label 945.2.a
Level 945
Weight 2
Character orbit a
Rep. character \(\chi_{945}(1,\cdot)\)
Character field \(\Q\)
Dimension 32
Newforms 14
Sturm bound 288
Trace bound 13

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.a (trivial)
Character field: \(\Q\)
Newforms: \( 14 \)
Sturm bound: \(288\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(945))\).

Total New Old
Modular forms 156 32 124
Cusp forms 133 32 101
Eisenstein series 23 0 23

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(20\)

Trace form

\(32q \) \(\mathstrut +\mathstrut 28q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 28q^{4} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 52q^{16} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 32q^{22} \) \(\mathstrut +\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 32q^{52} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 104q^{64} \) \(\mathstrut +\mathstrut 48q^{67} \) \(\mathstrut -\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 72q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 24q^{88} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(945))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7
945.2.a.a \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+q^{7}+\cdots\)
945.2.a.b \(2\) \(7.546\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-q^{7}+\cdots\)
945.2.a.c \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.d \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.e \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.f \(2\) \(7.546\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
945.2.a.g \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.h \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.i \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.j \(2\) \(7.546\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}+3q^{8}+\cdots\)
945.2.a.k \(2\) \(7.546\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-q^{7}+\cdots\)
945.2.a.l \(2\) \(7.546\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.m \(4\) \(7.546\) 4.4.144344.1 None \(-1\) \(0\) \(-4\) \(4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.n \(4\) \(7.546\) 4.4.144344.1 None \(1\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(945))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(945)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)