Properties

Label 354.3
Level 354
Weight 3
Dimension 1740
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 20880
Trace bound 1

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(20880\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(354))\).

Total New Old
Modular forms 7192 1740 5452
Cusp forms 6728 1740 4988
Eisenstein series 464 0 464

Trace form

\( 1740q + O(q^{10}) \) \( 1740q + 754q^{45} + 1392q^{46} + 1276q^{47} + 2088q^{49} + 1856q^{50} + 1624q^{51} + 696q^{52} + 1160q^{53} + 812q^{54} + 1044q^{55} + 290q^{57} - 232q^{59} - 348q^{60} - 696q^{61} - 464q^{62} - 1450q^{63} - 2436q^{65} - 1624q^{66} - 2088q^{67} - 1160q^{68} - 2552q^{69} - 2784q^{70} - 3016q^{71} - 1740q^{73} - 1856q^{74} - 986q^{75} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(354))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
354.3.b \(\chi_{354}(119, \cdot)\) 354.3.b.a 40 1
354.3.d \(\chi_{354}(235, \cdot)\) 354.3.d.a 20 1
354.3.f \(\chi_{354}(13, \cdot)\) 354.3.f.a 560 28
354.3.h \(\chi_{354}(5, \cdot)\) 354.3.h.a 1120 28

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)