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

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

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

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