↑

Properties

Label 1675.2.c
Level $1675$
Weight $2$
Character orbit 1675.c
Rep. character $\chi_{1675}(1274,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $11$
Sturm bound $340$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1675 = 5^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1675.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(340\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1675, [\chi])\).

Total New Old
Modular forms 176 100 76
Cusp forms 164 100 64
Eisenstein series 12 0 12

Trace form

\( 100 q - 94 q^{4} - 4 q^{6} - 96 q^{9} + O(q^{10}) \) \( 100 q - 94 q^{4} - 4 q^{6} - 96 q^{9} - 12 q^{11} + 16 q^{14} + 82 q^{16} + 16 q^{19} + 12 q^{21} - 16 q^{24} - 28 q^{29} - 8 q^{31} + 36 q^{34} + 50 q^{36} + 4 q^{39} - 16 q^{41} + 28 q^{44} + 8 q^{46} - 128 q^{49} - 48 q^{51} + 48 q^{54} - 68 q^{56} + 20 q^{59} + 12 q^{61} + 14 q^{64} - 120 q^{66} + 80 q^{69} - 24 q^{71} + 40 q^{74} - 124 q^{76} - 16 q^{79} + 84 q^{81} + 100 q^{84} - 32 q^{86} - 60 q^{89} - 64 q^{91} - 28 q^{94} + 92 q^{96} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1675.2.c.a 1675.c 5.b $2$ $13.375$ \(\Q(\sqrt{-1}) \) None 67.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+2iq^{3}-2q^{4}-4q^{6}-2iq^{7}+\cdots\)
1675.2.c.b 1675.c 5.b $2$ $13.375$ \(\Q(\sqrt{-1}) \) None 1675.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+2q^{4}+2iq^{7}-q^{9}+4iq^{12}+\cdots\)
1675.2.c.c 1675.c 5.b $2$ $13.375$ \(\Q(\sqrt{-1}) \) None 335.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-2iq^{7}+3q^{9}-2q^{11}+2iq^{13}+\cdots\)
1675.2.c.d 1675.c 5.b $4$ $13.375$ \(\Q(i, \sqrt{5})\) None 67.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(\beta _{1}+2\beta _{3})q^{3}+3\beta _{2}q^{4}+\cdots\)
1675.2.c.e 1675.c 5.b $4$ $13.375$ \(\Q(\zeta_{8})\) None 335.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{2}q^{3}-2q^{6}+2\zeta_{8}q^{7}+\cdots\)
1675.2.c.f 1675.c 5.b $4$ $13.375$ \(\Q(i, \sqrt{5})\) None 67.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1675.2.c.g 1675.c 5.b $4$ $13.375$ \(\Q(i, \sqrt{5})\) None 335.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1675.2.c.h 1675.c 5.b $14$ $13.375$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 335.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{10}-\beta _{13})q^{2}+(-\beta _{5}+\beta _{11})q^{3}+\cdots\)
1675.2.c.i 1675.c 5.b $16$ $13.375$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1675.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1675.2.c.j 1675.c 5.b $22$ $13.375$ None 335.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1675.2.c.k 1675.c 5.b $26$ $13.375$ None 1675.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)