Properties

Label 3960.2.d
Level $3960$
Weight $2$
Character orbit 3960.d
Rep. character $\chi_{3960}(3169,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $10$
Sturm bound $1728$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3960.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1728\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3960, [\chi])\).

Total New Old
Modular forms 896 74 822
Cusp forms 832 74 758
Eisenstein series 64 0 64

Trace form

\( 74 q + 4 q^{5} + O(q^{10}) \) \( 74 q + 4 q^{5} - 6 q^{11} - 4 q^{25} - 28 q^{29} - 20 q^{35} + 12 q^{41} - 78 q^{49} + 52 q^{59} + 28 q^{61} + 16 q^{65} + 8 q^{71} - 56 q^{79} + 20 q^{85} - 52 q^{89} + 88 q^{91} - 72 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3960.2.d.a 3960.d 5.b $2$ $31.621$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots\)
3960.2.d.b 3960.d 5.b $2$ $31.621$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}+2iq^{7}-q^{11}+3iq^{13}+\cdots\)
3960.2.d.c 3960.d 5.b $2$ $31.621$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-i)q^{5}+iq^{7}+q^{11}+2iq^{17}+\cdots\)
3960.2.d.d 3960.d 5.b $6$ $31.621$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}-\beta _{5})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
3960.2.d.e 3960.d 5.b $6$ $31.621$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
3960.2.d.f 3960.d 5.b $8$ $31.621$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}-q^{11}+\cdots\)
3960.2.d.g 3960.d 5.b $10$ $31.621$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{9}q^{7}-q^{11}+(1+\beta _{2}-\beta _{5}+\cdots)q^{13}+\cdots\)
3960.2.d.h 3960.d 5.b $10$ $31.621$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{5}-\beta _{1}q^{7}+q^{11}+\beta _{9}q^{13}+\cdots\)
3960.2.d.i 3960.d 5.b $14$ $31.621$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{5}+\beta _{5}q^{7}-q^{11}+(\beta _{1}-\beta _{5}+\cdots)q^{13}+\cdots\)
3960.2.d.j 3960.d 5.b $14$ $31.621$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{5}+\beta _{5}q^{7}+q^{11}+(\beta _{1}-\beta _{5}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1980, [\chi])\)\(^{\oplus 2}\)