Properties

Label 2790.2.d
Level $2790$
Weight $2$
Character orbit 2790.d
Rep. character $\chi_{2790}(559,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $15$
Sturm bound $1152$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

Total New Old
Modular forms 592 76 516
Cusp forms 560 76 484
Eisenstein series 32 0 32

Trace form

\( 76 q - 76 q^{4} - 4 q^{5} + O(q^{10}) \) \( 76 q - 76 q^{4} - 4 q^{5} + 12 q^{11} + 8 q^{14} + 76 q^{16} + 16 q^{19} + 4 q^{20} - 12 q^{25} - 12 q^{26} - 4 q^{29} + 8 q^{34} - 8 q^{35} - 16 q^{41} - 12 q^{44} - 16 q^{46} - 92 q^{49} + 16 q^{50} + 36 q^{55} - 8 q^{56} - 32 q^{59} - 36 q^{61} - 76 q^{64} + 28 q^{65} - 32 q^{71} + 4 q^{74} - 16 q^{76} + 24 q^{79} - 4 q^{80} - 12 q^{85} + 20 q^{86} + 72 q^{89} - 64 q^{91} + 32 q^{94} + 24 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2790.2.d.a 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
2790.2.d.b 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
2790.2.d.c 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
2790.2.d.d 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
2790.2.d.e 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-1-2i)q^{5}+5iq^{7}+\cdots\)
2790.2.d.f 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(1-2i)q^{5}+iq^{7}+iq^{8}+\cdots\)
2790.2.d.g 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}+iq^{8}+\cdots\)
2790.2.d.h 2790.d 5.b $2$ $22.278$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}+iq^{8}+\cdots\)
2790.2.d.i 2790.d 5.b $4$ $22.278$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{2}-q^{4}+(-2-\zeta_{8})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots\)
2790.2.d.j 2790.d 5.b $6$ $22.278$ 6.0.11669056.1 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}+(1-\beta _{1})q^{5}+2\beta _{3}q^{7}+\cdots\)
2790.2.d.k 2790.d 5.b $6$ $22.278$ 6.0.3534400.1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-q^{4}+(1-\beta _{4})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.l 2790.d 5.b $8$ $22.278$ 8.0.2058981376.2 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-q^{4}+(1+\beta _{1}-\beta _{7})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.m 2790.d 5.b $8$ $22.278$ 8.0.619810816.2 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(\beta _{6}+\beta _{7})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.n 2790.d 5.b $12$ $22.278$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(\beta _{6}+\beta _{7}+\beta _{11})q^{7}+\cdots\)
2790.2.d.o 2790.d 5.b $16$ $22.278$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-q^{4}+\beta _{6}q^{5}-\beta _{1}q^{7}-\beta _{9}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)