Properties

Label 2790.2.a
Level $2790$
Weight $2$
Character orbit 2790.a
Rep. character $\chi_{2790}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $37$
Sturm bound $1152$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1152\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2790))\).

Total New Old
Modular forms 592 50 542
Cusp forms 561 50 511
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(19\)
Minus space\(-\)\(31\)

Trace form

\( 50 q - 2 q^{2} + 50 q^{4} - 2 q^{5} - 2 q^{8} + O(q^{10}) \) \( 50 q - 2 q^{2} + 50 q^{4} - 2 q^{5} - 2 q^{8} + 2 q^{10} - 8 q^{11} + 50 q^{16} + 4 q^{17} + 24 q^{19} - 2 q^{20} + 12 q^{22} + 8 q^{23} + 50 q^{25} + 4 q^{26} - 28 q^{29} - 2 q^{32} - 4 q^{34} - 8 q^{37} - 16 q^{38} + 2 q^{40} - 4 q^{41} + 20 q^{43} - 8 q^{44} + 16 q^{46} - 16 q^{47} + 50 q^{49} - 2 q^{50} + 24 q^{53} - 16 q^{55} - 16 q^{58} - 16 q^{59} + 12 q^{61} - 8 q^{62} + 50 q^{64} + 4 q^{65} + 16 q^{67} + 4 q^{68} + 16 q^{70} + 32 q^{71} + 28 q^{73} - 12 q^{74} + 24 q^{76} + 24 q^{77} + 16 q^{79} - 2 q^{80} - 12 q^{82} + 52 q^{83} + 24 q^{85} + 16 q^{86} + 12 q^{88} + 68 q^{89} + 72 q^{91} + 8 q^{92} - 8 q^{94} + 16 q^{95} + 12 q^{97} - 2 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2790))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 31
2790.2.a.a $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-3\) $+$ $+$ $+$ $+$ \(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.b $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $+$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
2790.2.a.c $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $+$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots\)
2790.2.a.d $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(-5\) $+$ $+$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.e $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $-$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.f $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.g $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $-$ \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.h $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
2790.2.a.i $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
2790.2.a.j $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $-$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{11}+\cdots\)
2790.2.a.k $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $-$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.l $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(3\) $+$ $-$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}+3q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.m $1$ $22.278$ \(\Q\) None \(-1\) \(0\) \(1\) \(4\) $+$ $+$ $-$ $+$ \(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.n $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(-5\) $-$ $+$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.o $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $-$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.p $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.q $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.r $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $-$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.s $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots\)
2790.2.a.t $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $-$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.u $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(3\) $-$ $-$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.v $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $-$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.w $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.x $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(-3\) $-$ $+$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.y $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(-3\) $-$ $-$ $-$ $-$ \(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.z $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{11}+\cdots\)
2790.2.a.ba $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
2790.2.a.bb $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bc $1$ $22.278$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bd $2$ $22.278$ \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $+$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.be $2$ $22.278$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $-$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.bf $2$ $22.278$ \(\Q(\sqrt{65}) \) None \(-2\) \(0\) \(2\) \(-1\) $+$ $-$ $-$ $-$ \(q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.bg $2$ $22.278$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.bh $2$ $22.278$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $+$ \(q+q^{2}+q^{4}+q^{5}+2\beta q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bi $3$ $22.278$ 3.3.148.1 None \(-3\) \(0\) \(-3\) \(0\) $+$ $-$ $+$ $-$ \(q-q^{2}+q^{4}-q^{5}+(\beta _{1}-\beta _{2})q^{7}-q^{8}+\cdots\)
2790.2.a.bj $4$ $22.278$ 4.4.17428.1 None \(-4\) \(0\) \(-4\) \(5\) $+$ $+$ $+$ $-$ \(q-q^{2}+q^{4}-q^{5}+(1-\beta _{2})q^{7}-q^{8}+\cdots\)
2790.2.a.bk $4$ $22.278$ 4.4.17428.1 None \(4\) \(0\) \(4\) \(5\) $-$ $+$ $-$ $-$ \(q+q^{2}+q^{4}+q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2790))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2790)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1395))\)\(^{\oplus 2}\)