Properties

Label 675.2.a
Level 675
Weight 2
Character orbit a
Rep. character \(\chi_{675}(1,\cdot)\)
Character field \(\Q\)
Dimension 25
Newforms 17
Sturm bound 180
Trace bound 11

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 675.a (trivial)
Character field: \(\Q\)
Newforms: \( 17 \)
Sturm bound: \(180\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(675))\).

Total New Old
Modular forms 108 25 83
Cusp forms 73 25 48
Eisenstein series 35 0 35

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

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(9\)
Minus space\(-\)\(16\)

Trace form

\(25q \) \(\mathstrut +\mathstrut 26q^{4} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut +\mathstrut 26q^{4} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 29q^{37} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 14q^{52} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 72q^{64} \) \(\mathstrut +\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut -\mathstrut 62q^{76} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut -\mathstrut 68q^{82} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut +\mathstrut 13q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(675))\) 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
675.2.a.a \(1\) \(5.390\) \(\Q\) None \(-2\) \(0\) \(0\) \(3\) \(-\) \(+\) \(q-2q^{2}+2q^{4}+3q^{7}+2q^{11}+5q^{13}+\cdots\)
675.2.a.b \(1\) \(5.390\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-5q^{11}+5q^{13}+\cdots\)
675.2.a.c \(1\) \(5.390\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}-q^{4}+3q^{8}+5q^{11}-5q^{13}+\cdots\)
675.2.a.d \(1\) \(5.390\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(q-2q^{4}-4q^{7}+5q^{13}+4q^{16}+8q^{19}+\cdots\)
675.2.a.e \(1\) \(5.390\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(q-2q^{4}+q^{7}-5q^{13}+4q^{16}-7q^{19}+\cdots\)
675.2.a.f \(1\) \(5.390\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(q-2q^{4}+4q^{7}-5q^{13}+4q^{16}+8q^{19}+\cdots\)
675.2.a.g \(1\) \(5.390\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}-q^{4}-3q^{8}-5q^{11}-5q^{13}+\cdots\)
675.2.a.h \(1\) \(5.390\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+q^{2}-q^{4}-3q^{8}+5q^{11}+5q^{13}+\cdots\)
675.2.a.i \(1\) \(5.390\) \(\Q\) None \(2\) \(0\) \(0\) \(3\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+3q^{7}-2q^{11}+5q^{13}+\cdots\)
675.2.a.j \(2\) \(5.390\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) \(-3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1-4\beta )q^{8}+\cdots\)
675.2.a.k \(2\) \(5.390\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots\)
675.2.a.l \(2\) \(5.390\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-6\) \(-\) \(-\) \(q+\beta q^{2}-3q^{7}-2\beta q^{8}-3\beta q^{11}-3q^{13}+\cdots\)
675.2.a.m \(2\) \(5.390\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(6\) \(+\) \(-\) \(q+\beta q^{2}+3q^{7}-2\beta q^{8}+3\beta q^{11}+3q^{13}+\cdots\)
675.2.a.n \(2\) \(5.390\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(q+\beta q^{2}+5q^{4}-3q^{7}+3\beta q^{8}+2\beta q^{11}+\cdots\)
675.2.a.o \(2\) \(5.390\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(6\) \(+\) \(-\) \(q+\beta q^{2}+5q^{4}+3q^{7}+3\beta q^{8}-2\beta q^{11}+\cdots\)
675.2.a.p \(2\) \(5.390\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots\)
675.2.a.q \(2\) \(5.390\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) \(3\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(1+4\beta )q^{8}+(5+\cdots)q^{16}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)