Properties

Label 1305.2.c
Level $1305$
Weight $2$
Character orbit 1305.c
Rep. character $\chi_{1305}(784,\cdot)$
Character field $\Q$
Dimension $70$
Newform subspaces $12$
Sturm bound $360$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1305.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(360\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

Total New Old
Modular forms 188 70 118
Cusp forms 172 70 102
Eisenstein series 16 0 16

Trace form

\( 70 q - 66 q^{4} + 4 q^{5} + O(q^{10}) \) \( 70 q - 66 q^{4} + 4 q^{5} - 14 q^{10} + 8 q^{11} - 8 q^{14} + 82 q^{16} + 20 q^{19} - 12 q^{20} - 12 q^{26} - 6 q^{29} - 40 q^{31} - 12 q^{34} + 4 q^{35} + 10 q^{40} + 20 q^{41} - 8 q^{44} + 56 q^{46} - 62 q^{49} + 10 q^{50} + 14 q^{55} + 8 q^{56} + 16 q^{59} - 44 q^{61} - 90 q^{64} + 10 q^{65} - 32 q^{70} - 24 q^{71} + 60 q^{74} - 84 q^{76} + 56 q^{79} + 52 q^{80} + 52 q^{85} - 4 q^{86} - 36 q^{89} + 8 q^{91} + 36 q^{94} + 12 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1305.2.c.a 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-1}) \) None 435.2.c.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+(2-i)q^{5}-2iq^{7}+\cdots\)
1305.2.c.b 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-1}) \) None 435.2.c.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots\)
1305.2.c.c 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-5}) \) None 1305.2.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+\beta q^{5}-2\beta q^{7}-5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.d 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-5}) \) None 1305.2.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-\beta q^{5}-2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.e 1305.c 5.b $4$ $10.420$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 145.2.b.a \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1305.2.c.f 1305.c 5.b $4$ $10.420$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 145.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1305.2.c.g 1305.c 5.b $4$ $10.420$ \(\Q(\zeta_{8})\) None 435.2.c.c \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+q^{4}+(1+2\zeta_{8})q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)
1305.2.c.h 1305.c 5.b $6$ $10.420$ 6.0.84345856.2 None 145.2.b.c \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
1305.2.c.i 1305.c 5.b $10$ $10.420$ 10.0.\(\cdots\).1 None 435.2.c.d \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1305.2.c.j 1305.c 5.b $10$ $10.420$ 10.0.\(\cdots\).1 None 435.2.c.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1305.2.c.k 1305.c 5.b $12$ $10.420$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1305.2.c.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
1305.2.c.l 1305.c 5.b $12$ $10.420$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1305.2.c.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)