Properties

Label 1449.2.a
Level $1449$
Weight $2$
Character orbit 1449.a
Rep. character $\chi_{1449}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $20$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1449))\).

Total New Old
Modular forms 200 54 146
Cusp forms 185 54 131
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.

\(3\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(23\)
Minus space\(-\)\(31\)

Trace form

\( 54q + 52q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 54q + 52q^{4} - 8q^{5} + 6q^{8} + 12q^{10} + 8q^{11} - 8q^{13} + 64q^{16} - 4q^{17} - 12q^{19} + 8q^{20} + 4q^{22} + 6q^{23} + 34q^{25} + 26q^{26} + 8q^{31} + 12q^{32} - 44q^{34} + 8q^{35} + 8q^{38} + 8q^{40} + 24q^{43} + 12q^{44} - 4q^{46} + 8q^{47} + 54q^{49} - 16q^{50} - 42q^{52} - 24q^{53} + 28q^{55} - 30q^{58} + 20q^{59} + 4q^{61} + 30q^{62} + 78q^{64} - 20q^{65} - 12q^{67} - 36q^{68} + 20q^{70} + 16q^{71} - 72q^{73} - 20q^{74} + 4q^{76} - 4q^{79} + 76q^{80} + 6q^{82} - 16q^{83} - 64q^{85} + 40q^{86} + 8q^{88} - 36q^{89} - 12q^{91} + 12q^{92} - 70q^{94} - 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 23
1449.2.a.a \(1\) \(11.570\) \(\Q\) None \(-2\) \(0\) \(-4\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots\)
1449.2.a.b \(1\) \(11.570\) \(\Q\) None \(-2\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots\)
1449.2.a.c \(1\) \(11.570\) \(\Q\) None \(-2\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q-2q^{2}+2q^{4}+q^{7}-q^{11}+2q^{13}+\cdots\)
1449.2.a.d \(1\) \(11.570\) \(\Q\) None \(1\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots\)
1449.2.a.e \(1\) \(11.570\) \(\Q\) None \(2\) \(0\) \(2\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots\)
1449.2.a.f \(2\) \(11.570\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(3\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots\)
1449.2.a.g \(2\) \(11.570\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-5\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(-3+\beta )q^{5}+\cdots\)
1449.2.a.h \(2\) \(11.570\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
1449.2.a.i \(2\) \(11.570\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
1449.2.a.j \(2\) \(11.570\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(5\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}-q^{7}+\cdots\)
1449.2.a.k \(2\) \(11.570\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(5\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(2+\beta )q^{5}+q^{7}+\cdots\)
1449.2.a.l \(3\) \(11.570\) 3.3.837.1 None \(0\) \(0\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
1449.2.a.m \(3\) \(11.570\) 3.3.148.1 None \(1\) \(0\) \(-2\) \(-3\) \(-\) \(+\) \(+\) \(q+(\beta _{1}+\beta _{2})q^{2}+(1+2\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1449.2.a.n \(4\) \(11.570\) 4.4.2624.1 None \(-2\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1449.2.a.o \(4\) \(11.570\) 4.4.15317.1 None \(-2\) \(0\) \(-5\) \(-4\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
1449.2.a.p \(4\) \(11.570\) 4.4.24197.1 None \(0\) \(0\) \(-5\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
1449.2.a.q \(4\) \(11.570\) 4.4.2624.1 None \(2\) \(0\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1}+\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1449.2.a.r \(5\) \(11.570\) 5.5.2147108.1 None \(-2\) \(0\) \(4\) \(5\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{5}+\cdots\)
1449.2.a.s \(5\) \(11.570\) 5.5.1337792.1 None \(0\) \(0\) \(-4\) \(-5\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1449.2.a.t \(5\) \(11.570\) 5.5.1337792.1 None \(0\) \(0\) \(4\) \(-5\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1449))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1449)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)