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Properties

Label 2940.2.bb
Level $2940$
Weight $2$
Character orbit 2940.bb
Rep. character $\chi_{2940}(949,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $10$
Sturm bound $1344$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

Total New Old
Modular forms 1440 80 1360
Cusp forms 1248 80 1168
Eisenstein series 192 0 192

Trace form

\( 80 q - 2 q^{5} + 40 q^{9} + 8 q^{11} - 4 q^{15} - 8 q^{19} - 20 q^{25} - 40 q^{29} + 4 q^{39} - 48 q^{41} + 2 q^{45} - 4 q^{51} + 40 q^{55} + 28 q^{59} + 32 q^{61} - 10 q^{65} + 24 q^{69} + 104 q^{71} + 8 q^{75}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2940.2.bb.a 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 420.2.k.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
2940.2.bb.b 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 2940.2.k.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{3}+(\zeta_{12}-2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
2940.2.bb.c 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 420.2.k.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
2940.2.bb.d 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 60.2.d.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
2940.2.bb.e 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 60.2.d.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(1-2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
2940.2.bb.f 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 420.2.k.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
2940.2.bb.g 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 2940.2.k.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
2940.2.bb.h 2940.bb 35.j $4$ $23.476$ \(\Q(\zeta_{12})\) None 420.2.k.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
2940.2.bb.i 2940.bb 35.j $16$ $23.476$ 16.0.\(\cdots\).1 None 420.2.bb.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{6}+\beta _{7})q^{3}+(-\beta _{8}+\beta _{13})q^{5}+\cdots\)
2940.2.bb.j 2940.bb 35.j $32$ $23.476$ None 2940.2.k.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)